The Dink Network

I gave up to the Computers National Olimpiad

March 22nd 2006, 02:23 PM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
It's true. I was the first at the county phase at physics, math and computers. Since they are in the same week(in different cities), I had to choose. First, I gave up to physics. Now, I heared that computers will be on 16 and 17 april, while math on 17. I had to choose between them too.
Arghhhh...
March 22nd 2006, 05:47 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
Bleh, I hate it that I never got to participate in the math olympiad. Good luck.
March 23rd 2006, 01:28 PM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
Thanks. I'll send you the problems if you want. Tommorrow I'm going to another math contest, a inter-county one. Wish me luck.
March 23rd 2006, 02:02 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
If they're English, please do Again, good luck.
March 23rd 2006, 02:10 PM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
They're not, but I'll translate them for you.
March 26th 2006, 02:36 PM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
I'm back. I was the second, with 25.5/28(while the first had only 26 ). I won 200 RON(about 60$), and I also won a special prize of originality. It was a portable MP3 Player .
The next contest will be the Math National Olympiad, in about three weeks.
@magicman: I'll send you the problems in a few days on PM.
March 26th 2006, 02:58 PM
fish.gif
Simeon
Peasant He/Him Netherlands
Any fool can use a computer. Many do. 
Can't you post them here? I'm not a mathematical genius but ah well - and more people can read them anyway
March 27th 2006, 06:59 AM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
Ok. Hope you'll understand my "English math".
1. The three points X(5,4,0), Y(3,0,2), Z(1,8,4), are the vertex of a cube. Find it's center.

2. m is a natural number, and the function F:M2(C)->M2(C), F(X)=X^m.
Prove that F is surjective if and only if m=1.

3. f:R->R is a function, and there exists L>0, so |f(x)-f(y)|>=L|x-y|, for every x,y, that belongs to R.
Prove that f is surjective if and only if f is continous.

4. Find all the continous functions g:R->R, with the following property: for every x that belongs to R, there exists a,b that belongs to (0,1), a+b=1, so g(x)=a*g(ax)+b*g(bx).(a and b aren't necessary the same for every x)

The first one was way too easy and the secod one was quite easy too.(I took 7/7 on both of them). The third one wasn't difficult, but it seems that I wasn't 100% rigurous(only 6.5/7). The last one was pretty difficult, but I managed to obtain 5 points(and I think the special prize I obtained was for this). I won't tell you yet how I solved them, I'll let you think a while on them.
March 27th 2006, 12:14 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
That looks a lot like Analysis... something at which I suck.

One question, though... something about notation. What is meant by M2(C)?

I will start figuring them out when I get home... and when I'm not asleep or equivalent.
March 27th 2006, 01:12 PM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
M2(C) is a matrix that has two lines and two collumns, and it contains complex numbers.
I suck too at analysis, but the 3rd problem really wasn't difficult(the 4th was).
March 27th 2006, 04:48 PM
dragon.gif
Ummm... I haven't learnt that level of mathematics yet and I doubt many people here have. I also don't intend to learn that level of mathematics and I doubt many here want to.

To me that seems as foreign as the any of the Star watrs and Star Trek languages.
March 27th 2006, 04:54 PM
dragon.gif
Arg! I hate complex numbers! They aren't even real numbers! To quote my maths tutor here at Uni: "complex numbers are things like the square root of -2". That's an imaginary number! You can't get a even root of a negative number! Not unless you invent some rubbish concept like "complex" numbers. More like non-existant numbers if you ask me. There is no logical even root of a negative number! And maths is supposed to be about and be based upon logic! Not illogical things like even roots of a negative numbers! So the invention (and thats what it is) of "complex" numbers annoys me. It defies how mathematics is supposed to work.
March 28th 2006, 06:09 AM
fish.gif
Simeon
Peasant He/Him Netherlands
Any fool can use a computer. Many do. 
The maths here looks sorta like the one I've had in the beginning of this year or in the previous course about logic and set theory. In theory, I should be able to solve 1 and 2.. for the two others I don't know the mathematical definition of "continuous" so I don't really know how to start there - I know what it means but it's usually easier to take the mathematical definition and work from there (like "for all a in set A ,there is a b in set B etc") And I'm not that good at proving things in mathematics anyway
March 28th 2006, 06:20 AM
fish.gif
Simeon
Peasant He/Him Netherlands
Any fool can use a computer. Many do. 
Actually in the "Vakidioot" magazine which the beta-students here receive every now and then, there was an interesting article about the invention and history of complex numbers. And it kinda makes sense to keep calculating with numbers that don't make sense.. as you still get useful results in the end

I'm surprised I read it, as a computer science student I should've read the article about virtual machines (which I read too but that was less interesting )
March 28th 2006, 11:37 AM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
Quaternions, nuff said...

Complex numbers make sense. In a way, i can be seen as a second axis in two-space. In this way, multiplying by i means rotating a vector 90 degrees. It can be really useful if you don't want to (directly) deal with polar coördinates. And physicists use it to describe oscillations, among other things.

Even with i added, the basic laws of the Real numbers still hold: a*b = b*a, a+b = b+a, a*(b*c) = (a*b)*c, (a+b)+c = a+(b+c), a*(b+c) = a*b + a*c. And really, why wouldn't there be a square root of a negative number? Why would (a little less than) half of our "known" real numbers be left out of the joy of having a square root? That's just rubbish! It's like saying "and you can't be devided by two". Really, people before thought that wasn't possible, but then they invented some silly notation like 1/2 to make up for it, and called it Rational Numbers for no apparent reason other than to (basically) solve 2*x==1. Why wouldn't x²+1==0 haven't got any solutions? If we can invent something, and still keep things consistent, why shouldn't it?

I keep saying "consistent" and such, because such a number "u" for 1/0 can't exist. It has been proven already by several classmates of mine. 0^0 will get you into problems too.
March 28th 2006, 11:39 AM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
(For the flat-people, this is no double post)

Definition of continuous:

f : R -> R is continuous if and only if
lim (x->a) f(x) = f(a),
for all a in R

Now the definition for a limit, shall I? Nahh

EDIT: Thanks Simeon, yes it was an iff.
March 28th 2006, 01:29 PM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
First of all, the second problem doesn't involves any complex number theory. It could have been R,Q,Z, even N. It would have been the same.
The comlex numbers are use often in geometry, because it's easier to use them instead of vectors(although there aren't great differences).
About analysis, I thought Simeon and DraconicDink were at University. I'm just in the third year of highschool and I started analysis this year.
March 28th 2006, 01:42 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
We don't do much of this abstract analysis in highschool. My third year math consisted of sines, cosines drawing parabola, calculating where the top of a parabola is (without knowing anything about derivatives, what a torturous time). Also we weren't allowed to enter the olympiads before the fifth.

But now I look at your profile, I see you're 17. That's what I was in the last year of highschool/first few months Uni, so I guess our school systems are very different.
March 28th 2006, 02:13 PM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
But now I look at your profile, I see you're 17
That makes me think I should change my profile. I wrote it last summer, when I wasn't 17 yet. I'll be 18 this year in october(I'm exactly one year younger than Tal).
Also we weren't allowed to enter the olympiads before the fifth.
You mean the fifth year of school, right? Because it's the same thing here. The third year of highschool is the 11th per total.
March 28th 2006, 02:20 PM
fish.gif
Simeon
Peasant He/Him Netherlands
Any fool can use a computer. Many do. 
I assume that if is an iff (if and only if)? I won't nitpick but thanks.. this doesn't guarantee I can solve it though
March 28th 2006, 02:27 PM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
Did you managed to solve the first two?
March 28th 2006, 02:34 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
Fixed, thanks
March 28th 2006, 04:40 PM
dragon.gif
And it kinda makes sense to keep calculating with numbers that don't make sense

That doesn't make any sense! It's a contradiction! And to quote the Wizards Nineth Rule from Chainfire, book nine of the Sword of Truth series: Contradictions cannot exist in reality.

To add to that: contradicitons exist only in what people say or think. For what you say to be real it needs to be non-contradictory. In other words, you are either wrong or have a good point but used bad wording. In light of the part of your statement that followed, i'll assume it was a good point with bad wording. One that should of been worded in a non-contradictory way.

However, what use do we have for trying to figure out the square root of -2?

I would also like to point out the fact that things like the square root of -2 are quite accuretly refered to in maths as a "imaginary number", not just a "complex number".
March 28th 2006, 04:48 PM
dragon.gif
And really, why wouldn't there be a square root of a negative number? Why would (a little less than) half of our "known" real numbers be left out of the joy of having a square root? That's just rubbish!

It's not rubbish. If you say "what is the square root of X?" you are in fact also saying "what number multiplied by itself equals X?" So if X is a negative number you a question that has no logical answer. Here is why:

- Say X is 4.
- The square roots of 4 are 2 and -2.
- However is X is -4 the same does not hold. Here is why:
* Positive times positive = positive * Whenever you multiply a even number of negatives you get a positive number.

In other words -X has no even root. It does however have a odd root.

In short, no real numbers exist that give us -X when they have a even power. Meaning -X squared does not have a logical answer if you use real numbers. Hence complex numbers also being called "imaginary numbers".

as for being consistent, i think the above information makes it clear that constiency is laking when you try to use real numbers.
March 28th 2006, 04:59 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
With Complex numbers there is no positive and negative. There is no x > y (that is, unless x = r*y, with r a real number, because then you could say x > y if r > 1 (or maybe if |r| > 1)). Only an |x| > |y| would exist for any two complex numbers x and y, so your statement makes no sense.

Of course there are no real numbers that give -X when they have an even power. There aren't any natural numbers that give 3 when they are multiplied by 2. That's why they added i and 1/2.

When would you say a number exists? Why would 2 exist? Why Sqrt(2)? Why pi-log(14)? Why 3/4? Why not 2i + 6?

EDIT: before you're going to nitpick about the word "exists", I mean, why is i "imaginary" and all those others not?
March 28th 2006, 06:02 PM
pq_water.gif
Its interesting from a philosophical point of view too DD... the definitions between real and 'unreal'... and the components that make up the whole... and as for contradictions, they exist all around us... just gives us some more to think about as we wander along...
March 28th 2006, 07:29 PM
dragon.gif
With Complex numbers there is no positive and negative. There is no x > y (that is, unless x = r*y, with r a real number, because then you could say x > y if r > 1 (or maybe if |r| > 1)). Only an |x| > |y| would exist for any two complex numbers x and y, so your statement makes no sense.

No neagtive and positive? That is not consistent with the rest of maths! It also isn't logical! Which proves my point that it defies the way maths is supposed to work (logically, that is).

When would you say a number exists? Why would 2 exist? Why Sqrt(2)? Why pi-log(14)? Why 3/4? Why not 2i + 6?

I cannot answer that question since I have no idea what those examples mean. In High School (usually called College here) I didn't pass any areas beyond the level of algrbra (which is easy).
March 28th 2006, 07:32 PM
dragon.gif
In my high school years I couldn't understand anything more advanced than Calculus. That's why I don't understand a lot of this stuff. And the maths paper I'm doing is Bridging Mathematics and Statistics, so it doesn't cover complex numbers so I won't be learning that about part of this discussion in my studies.
March 28th 2006, 07:35 PM
dragon.gif
(For the flat-people, this is no double post)

Definition of continuous:

f : R -> R is continuous if and only if
lim (x->a) f(x) = f(a),
for all a in R

Now the definition for a limit, shall I? Nahh

EDIT: Thanks Simeon, yes it was an iff.


That still goes way over my head.
March 28th 2006, 07:42 PM
dragon.gif
If reality contradicted itself it wouldn't exist. Logical thinking (forget my usual statements of rational thinking because you don't even need to go to that lvel, logic will do) tells us this. But if reality doesn't exist how could I be saying this? And isn't the definition of reality "that which exists"?

To put in prospective I'll give an obvious example: squares has four even sides. If we see something with round we cannot realistically say it is a aquare because it has no sides. There can be no contradiction of a case of a square with more or less than four even sides.

I know that's a simplistic case and many of you will say it's different with other things, but here's my pre-response: no it isn't.

Also I'm curious to see if you can come up with any examples at all let alone realistic ones.
March 28th 2006, 08:57 PM
custom_king.png
redink1
King He/Him United States bloop
A mother ducking wizard 
Negative numbers? That is not consistent with the rest of maths! It also isn't logical! You can have 2 apples, but you can't hold -2 apples!! And what if you multiply two negative numbers together, like -2 * -2. That equals a positive 4? That isn't rational!

That proves my point that negative numbers defy the way maths is supposed to work (logically, that is).

Note: My intention isn't purely to mock you, but it is to show you that things may not appear to be logically correct when you have a limited comprehension and understanding of the concept. Negative numbers are useful just as imaginary numbers are useful.
March 29th 2006, 08:51 AM
pq_water.gif
And any thought DD, even proven erroneous, has value from a philosophical standpoint. Consider the shades of grey for once.
March 29th 2006, 01:29 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
If the definition of reality is "that which exists", then what is the definition of "something that exists"?
March 29th 2006, 02:21 PM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
You can have 2 apples, but you can't hold -2 apples!! And what if you multiply two negative numbers together, like -2 * -2. That equals a positive 4? That isn't rational!
You can't hold 2 apples, but you can owe somebody 2 apples(-2). If two people owes you two apples each( (-2)*(-2)=4 ), that means you'll have 4 apples.
Negative numbers are useful just as imaginary numbers are useful.
Let's take electricity for example. There can be pozitive or negative charges of electricity. That's a pretty usefull application of negative numbers.
It is said that the only part of math that has no practical applications yet is the numbers theory(prime numbers and such).
March 29th 2006, 02:40 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
The best assymetric encryption algorithms (as well as many other ones) are possible thanks to our knowledge of number theory.
March 29th 2006, 03:01 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
No neagtive and positive? That is not consistent with the rest of maths!

Not consistent? You ignorant fool! You might not be a fool, but you sure are ignorant. Which of the following mathematical objects (actually vectors in a 2D world, like coördinates on a map, with 0=(0,0) in the middle) is larger: (1,-1) or (1,1)? Also, is (1,-1) larger than (0,0) or smaller? What about (-1,1)?

You possibly can't answer these questions, but that's okay, they have no answer. While the length of both (1,-1) and (-1,1) is certainly larger than the length of (0,0), still (1,-1) = -(-1,1). So we have point X and point Y of which X and Y are larger than 0, X = -Y, so X + Y = 0. That's a contradiction! That's not logical! Inconsistent! Irrational! There are no 2D coördinate systems! The ground on which we walk can't be described! To heck with maps! To heck with depth! There's only one line of movement!

If they do exist, think of a complex number a + bi to actually be the vector (a,b), and that multiplication of vectors is defined as (a,b)*(c,d) = (ac - bd, cb + ad). Even if you see real numbers r and as vectors (r,0) and (s,0) in 2D, this holds, as b and d are 0. Even if you want to scale (shorten or lengthen, without changing direction) a 2D vector (a,b) with a real number c = (c,0), this holds, as d would be 0.

I cannot answer that question since I have no idea what those examples mean.

Cheap, you didn't even try. At the very least you could answer the question for the examples of which you have an idea.

I'm pretty sure you know about 2, Sqrt(2) (Sqrt == Square root)and 3/4. 2i + 6 is just a random complex number. If you really want to know, pi-log(14) is the solution to
pi^x = 14
and pi is about 3.1415 etc...

pi-log(14) is approximately 2.305, but nobody in their right mind would ever want to calculate it. Technically, it exists, though.

EDIT: Hmm... I could've merged those last two posts... even in nested they show up right after eachother.
March 29th 2006, 05:46 PM
dragon.gif
Negative numbers are not irrational. They tell us things like loss in business. Is that not real. a loss of $200 is the equivalent of -$200 profit. That is real and rational, therefore so are negative numbers.

yes your example of -2 apples is correct, but negative numbers can work in logical cases like the above money one.
March 29th 2006, 05:47 PM
dragon.gif
dang good point there about negative numbers, Crypy.
March 29th 2006, 05:50 PM
dragon.gif
That's obvious. Self-evident things. Example: we obviously exist, or we wouldn't be having this conversation. Our existence is self-evident. The same goes for earth, else we'd have no location in which to have the conversation, meaning we wouldn't be having it. Thus, Earth's existance is self-evident.
March 29th 2006, 05:52 PM
dragon.gif
And any thought DD, even proven erroneous, has value from a philosophical standpoint. Consider the shades of grey for once.

Sorry but I disagree with that. It's irrational. Philosophy is about trying to evualate the nature of reality/existence. How can an erroneous thought have any value except to be tell us where not to go? Since that can be done with the right kind of thinking there is no use for it so there is no value.
March 29th 2006, 06:02 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
So how do you know a number exists?

EDIT: Please to not reply (maybe delete) as this is issued in my über-reply at, what is at the time of this writing, the bottom of the thread.
March 29th 2006, 06:11 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
You make a lot of wrong points to which I have something to say. But instead of writing 5 replies (as I'd usually do), I decided to quote up a few things and paste them into an über reply.

Philosophy is about trying to evualate the nature of rea;ity/existence.

You can try to evaluate a false nature of reality/existence. It will evaluate to false. Trivial, but true. Because you can try to evaluate it, it has part in philosophy. Also, if we do not know yet where to go, but we know at least one way not to go, we can eliminate that way and focus on other ways of which we aren't sure.

That's obvious. Self-evident things.

Then in what way could a number be self evident? A number is just some weird way to write an abstact concept which can be used for (at least) quantity (amount, length, mass, etc), proportion, location, amongst other things of which we might not know they exist. That I know more uses for a number, and have need for more numbers, than you, is your ignorance, not my brain gone wrong.

ADDITION TO THIS PART: What I mean to say, is that a number can only exist if there's a use for it. I can say I have this cool new number "1", but not be able to use it. Why the heck would I have this "1" to begin with?

Negative numbers are not irrational.

-1*Sqrt(2) is irrational. Sorry, math pun.
March 30th 2006, 12:21 PM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
I have a cool new number: 15873. What should we do with it? Try multiply it by a digit(1..9), then multiply the number obtain by 7. This is quite a usefull number, right?
Now, I'm gonna prove that there are no uninteresting/unusefull natural numbers:
Let's pretend there exists uninteresting numbers. Then, we can split all the natural numbers into 2 sets. The interesting ones(A) and the uninteresting ones(B). Obviosly, the set B will have a minimum. Then, that minimum, will be the lower uninteresting number, wich suddenly becomes interesting. - contradiction. That means that there are no uninteresting numbers.
March 30th 2006, 02:41 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
Your 'new' 15873 already exists. It corresponds with the 15873 of the natural numbers (and supersets thereof). My '1' is just a notation for a certain element of a certain set, on which there might not even be such a thing as multiplication.

---

I think the general confusion in the math-part of this thread, is that most of you have only done elementary algebra, while this is just a tiny little part of universal algebra (or sometimes just called algebra). Elementary algebra is just a special case of universal algebra, and many of the known, 'obvious', laws in elementary algebra aren't as obvious as they seem in universal algebra. In the broadest sense of the word, "algebra" is the study that deals with sets 'A', combined with (for every set 'A') a collection of operations on A.

Elementary algebra stops at the real axis, not covering complex sets, matrix sets, or even the general terms for these: fields, rings, groups, monoids, etc. Therefor, most people who are known to only a tiny bit of the universal algebra would say other things cannot be, while what they consider a definition to be generally true, is just a definition on the sets it's defined on, because they only know a part of all sets that can possibly be defined, the definitions don't have to be true for those other sets.

For example, (the very same example that lead to this discussion) there are no real numbers x so that x^2 = -1, is true. Stating that there are no numbers x in general so that x^2 = -1, isn't true. Just find a collection of elements, with an operation *, define the notation x^2 to be x*x (so we won't need to have 2 in our set), and define * so that we have an element 'x' and an element '-1', so that x*x = -1. Then there suddenly ís a number so that x^2 = -1.

Another thing that can lead to confusion is the mathematical term for different sets. "natural" numbers, "rational" numbers "real" numbers. When DraconicDink said that negative numbers aren't irrational, he meant a different "irrational" than what algebra-people (algebraicians?) would consider "irrational" (and even more different from what a game theorist would consider "irrational"). DraconicDink's references to "real" numbers as "numbers which exist" is also different from what mathematicians consider "real" numbers. I don't think a number on itself exists. It's always part of a certain algebra, that is, part of a set, on which an operation is defined. Same thing with "natural" numbers. While it might sound like "natural" means "obvious" (which would be a 'natural' line of thought, if you get what I mean), the "natural" numbers aren't quite as obvious as they might seem.

Quick overview (of how mathematicians see things):
Natural numbers
Integers
Rational numbers
Real numbers
---
Complex numbers
--- Stop reading here, unless you really want to dig into advanced algebra stuff
Quaternions
Octonions
Sedenions

Of which the last three are more extreme algebras.
Quaternions don't have a commutative multiplication. This means that for *-for-quaternions the following isn't always true: a*b = b*a
Octonions don't have a commutative multiplication either, but no associative multiplication. This means that a*(b*c) can be different than (a*b)*c. Though it's still true that a*(a*b) = (a*a)*b
The sedenions's multiplication isn't even alternative, which means that a*(a*b) = (a*a)*b.
They are all still power associative, which means that a*(a*a) = (a*a)*a. I haven't found an algebra yet for which this is not true, but I won't exclude anything.

If you're interested in these algebraically beautiful anomalies, you might want to check out free objects. Those are algebras, with one binary operation (operation with two input-variables and one output variable) in which as many axioms and relations between elements are thrown away. I'm possibly the only one here, but I really like to brag about my universitary study, and how I get these things
March 30th 2006, 02:57 PM
fish.gif
Simeon
Peasant He/Him Netherlands
Any fool can use a computer. Many do. 
Nice post! Mathematics is quite interesting actually but studying it would've killed me But I'm doing computer science so I do get to touch it every now and then (set theory, the rules of logic (axioms, propositions and predicates) and basic mathematical operations on matrices, vectors, complex numbers and equations with several unknown variables). It's more the way a mathematical language defines/proves things unambiguously that I appreciate about maths, even though I'm not that great at calculating or proving things myself.

But it's still interesting like funny things about numbers/mathematical tricks.. the one I recently heard of was about the number 196. For most natural numbers, you can do the following and always end up with a palindrome.. but for 196 it hasn't been proven that it will result in a palindrome:

1. Take a natural number (e.g. 431)
2. Revers the digits (134)
3. Add (431 + 134 = 565 = palindrome)
4. If not palindrome, goto 2

March 30th 2006, 04:01 PM
dragon.gif
You can try to evaluate a false nature of reality/existence. It will evaluate to false. Trivial, but true. Because you can try to evaluate it, it has part in philosophy. Also, if we do not know yet where to go, but we know at least one way not to go, we can eliminate that way and focus on other ways of which we aren't sure.

That does not prove me wrong in any way, since deciding what is not real/correct is in fact a part of deciding what is real/correct, meaning that what you said is a process of what I was referring to, not proof against it.

Then in what way could a number be self evident?

I never said numbers exist. I said "real numbers". When I said that it was not meant literally. It was meant in a more metaphorical way. Numbers do not exist in a literal sense, only ammount. And as you say numbers are a way representing amoount. Numbers are way of saying X ammount of a certain unit (eg: amoount = five, unit = apples).

That I know more uses for a number, and have need for more numbers, than you, is your ignorance, not my brain gone wrong.

Firstly I never said there was anything wrong with the brain of anyone here. Secondly a lack of use, does not equal ignorance. Ignorance is a lack of understanding. My ignorance is in that I do not know much about imaginary numbers, not in my having no use for them. The lack of use for them springs from the fact that I won't be doing anything that has a use for them. For exmple: an author of fantasy books has no need for knowing the square root of -5, thus that aspect of my life has no need for it. The other aspects of my life are the same, lacking in the need for it.

-1*Sqrt(2) is irrational. Sorry, math pun.

I don't know what Sqrt means, but let me clarify (with the clarification is itallics so it stands out) my point since you don't seem to understand: negative numbers are not irrational when by themselves or with [i]positive numbers or simplistic maths (stopping at algrebra). In fact they are rattional in that case, since as I said they are useful to represent thing like a loss of money (money owed, or simply that this year's gross earning's for Example Ltd, leaving them with just $5000). Remember that a negative number is simply the same as subtracting a positive number. Subtracting a positive number is rational, so why can't a negative number be rational?
March 30th 2006, 04:12 PM
dragon.gif
Another thing that can lead to confusion is the mathematical term for different sets. "natural" numbers, "rational" numbers "real" numbers. When DraconicDink said that negative numbers aren't irrational, he meant a different "irrational" than what algebra-people (algebraicians?) would consider "irrational" (and even more different from what a game theorist would consider "irrational"). DraconicDink's references to "real" numbers as "numbers which exist" is also different from what mathematicians consider "real" numbers. I don't think a number on itself exists. It's always part of a certain algebra, that is, part of a set, on which an operation is defined. Same thing with "natural" numbers. While it might sound like "natural" means "obvious" (which would be a 'natural' line of thought, if you get what I mean), the "natural" numbers aren't quite as obvious as they might seem.

Actually I mean exactly what mathematicians consider "real" numbers. In my maths paper my tutor said: "that complex numbers can also be called 'imaginary numbers' and that they are things like the square root of -4, which has no logical answer". He also said that a "real number" is a number which has a logical answer to it, for example, such as the square root of 4. I agree with you that numbers themselves do not exist. When i said "real numbers" I did not mean "real" literally. Numbers are simply a human concept that was invented to represent a X ammount of a certain unit (eg: ammount = 10, unit = dollars).

However, I agree with your point on natural numbers. For those of you that don't know (if there are any): natural numbers are whole numbers (1,2,3...), not "obvious" numbers. So 1.2, 2.5, 3.9... are not natural numbers.
March 30th 2006, 04:14 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
That does not prove me wrong in any way,

Quote: "And any thought DD, even proven erroneous, has value from a philosophical standpoint. Consider the shades of grey for once."

Sorry but I disagree with that. It's irrational. Philosophy is about trying to evualate the nature of reality/existence.


You there said you disagreed to that proven erroneous thoughts have value from a philosophical standpoint. Next you say that philosophy is about trying to evaluate the nature of reality/existence. Then I prove that even proven erroneous thoughts are a part of trying to evaluate the nature of reality/existence, with which I prove that proven erroneous thoughts are a part of philosopy, so they have a value (which can be negative, but they still have a value), thus proving against your first statement that proven erroneous thoughts don't have value from a philosophical standpoint.

Firstly I never said there was anything wrong with the brain of anyone here.

Firstly, I never said you ever said there was anything wrong with the brain of anyone here.

Secondly a lack of use, does not equal ignorance.

Secondly, I never talked about a lack of use, only about you not knowing uses. I.e. lack of understanding how you can use numbers. Which is a lack of understanding, which is ignorance, by your own definition.

I don't know what Sqrt means,

Read a few posts above, where I say: "Sqrt == Square root"

(stopping at algrebra)

You here mean elementary algebra. As if you had actually followed the links, you had seen that, what you consider irrational (your def, not mine... more about this later) complex numbers, are a part of universal algebra, and thus part of algebra, and thus part of math. It's just that all elementary algebra is part of universal algebra, but not vice-versa.

Also, I said confusion is caused by our different definitions of rational/irrational. As I said I don't believe in numbers to just exist, nor that quantity is the only use for a number. I have no possible way to say if a number is rational (your def), because I have no possible way to say if a number is at all. I do not disagree nor agree to if numbers are rationar/irrational according to your definition of rational/irrational. What I know for sure is that -1*Sqrt(2) is irrational from my definition if irrational, which is not rational. That's also your definition, but my definition of rational is different than yours. Mine is:
A number is rational if it can be written as a/b, with a an integer and b a non-zero integer.

It was a pun anyway, and one non-mathematicians have trouble understanding, because it requires one to know the math-definition of rational, which many non-mathematicians don't know.
March 30th 2006, 04:16 PM
dragon.gif
I'm glad that the computer science i will be doing won't require things like vectors, etc, because I have no intrest or need for them.
March 30th 2006, 04:25 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
Crappy tutor you had, or at least crappy in non-elementary algebra (elementary algebra as in my other post). A good mathematician would, with a correct definition of imaginary number (which is exactly the same as complex number), say i and -i are logical answers to x^2 = -1.

Probably what he meant are computable numbers, which are real number (math def) per definition. Check this: Computable numbers.
March 30th 2006, 04:31 PM
dragon.gif
That does not prove me wrong in any way,

Quote: "And any thought DD, even proven erroneous, has value from a philosophical standpoint. Consider the shades of grey for once."

Sorry but I disagree with that. It's irrational. Philosophy is about trying to evualate the nature of reality/existence.

You there said you disagreed to that proven erroneous thoughts have value from a philosophical standpoint. Next you say that philosophy is about trying to evaluate the nature of reality/existence. Then I prove that even proven erroneous thoughts are a part of trying to evaluate the nature of reality/existence, with which I prove that proven erroneous thoughts are a part of philosopy, so they have a value (which can be negative, but they still have a value), thus proving against your first statement that proven erroneous thoughts don't have value from a philosophical standpoint.


Okay since you misunderstood me, let me clarify: I meant that after they have been proved they are useless. The taking them into account to know where not to go takes place during the discrediting not after.

Also i'd like to point out that you did not include all a statement that you quoted and that a part of it proves that meant it in the above way. To prove this I will extract that part and quote it below:

How can an erroneous thought have any value except to be tell us where not to go?[i]

This is the exact same thing as you said.

[i]Firstly, I never said you ever said there was anything wrong with the brain of anyone here.


Then why say That I know more uses for a number, and have need for more numbers, than you, is your ignorance, not my brain gone wrong.
? The part "not my brain gone wrong" indicates that you think I thought that.

Secondly, I never talked about a lack of use, only about you not knowing uses. I.e. lack of understanding how you can use numbers. Which is a lack of understanding, which is ignorance, by your own definition.

I was also saying that I do not have a lack of understanding, but simply disagree with the use, not only that it was not ignorance, hence that followed about my not having a use for it.

You here mean elementary algebra. As if you had actually followed the links, you had seen that, what you consider irrational complex numbers, are a part of universal algebra, and thus part of algebra, and thus part of math. It's just that all elementary algebra is part of universal algebra, but not vice versa.

I never said that they weren't a part of maths. I know that complex numbers are a part of maths. I just that they were not a logical part of maths, as quoted from the tutor of my maths paper. A illogical part of something is still a a part of it and I realise that, thus I never thought it wasn't a part of maths and always (since knowing about it) thought it was a part of maths. In short, you did not need to point out to me that it was a part of maths. Also, I did look at the links.
March 30th 2006, 04:41 PM
dragon.gif
(which is exactly the same as complex number)

i realise that and in fact said so many times.

Crappy tutor you had, or at least crappy in non-elementary algebra

You don't have enough yet information to know that. Here's why: we aren't up to universal algrebra yet (if we're covering it at all). We are only up to simplistic algrebra (multiplication, division, subtration, addition, roots and powers (including fractional and negative powers)). It would be a bad idea for him to confuse by going into universal algrebra at this point. To do so would in fact make him a "crappy tutor" as you put it. In fact in not going into a level above our understanding he is in fact a good tutor. We still have a lot to go in our algrebra section, but I don't think we'll be going into universal algrebra since he said "I am not going to teach you about complex numbers in this paper because this is a bridging mathematics paper, not an advanced mathematics paper. If you want to learn about advanced mathematics you can do that when you go onto doing your degree,as there are plenty of papers that cover it." Clarification: this paper is trying to cover Years 1-13 of maths in one semester, meaning that it has to leave a lot of more advanced stuff out due to time limits. Also due to what it is trying to due it is not neccessary for it to teach the more advanced stuff, especially since the university (and all others in the country) offer plenty of papers for people to learn those areas of maths from.
March 30th 2006, 04:53 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
i realise that and in fact said so many times.

I realise also that you realise it, and that I said it so many times. You just don't seem to realise that the existence or rationality (your def) of something doesn't suddenly change when you call it a different way.

LATE ADDITION TO THIS PART: Or you actually realise it, but you saying so many times that they're also called "imaginary" tends to lead me to believe otherwise.

You don't have enough yet information to know that

In the way you explain it, I agree, but not fully. Here's how I think:

In the math you know, and the tutor wants you currently to know, complex numbers don't exist, and are completely illogical, simply because they are not a part of the math you know, or you tutor wants you to know. Sadly I know this behaviour all too well from my old teachers. They would tell you things like "i isn't logical" (altough I don't believe he literally would deny any possibility of i ever to be logical), just to save some confusion. Understandable, though, as the normal stuff is quite touch already (as you said 13 years in one semester is impressive).

Don't get me wrong, I think he did well to tell you you should forget about complex numbers, as you already indicated you have no interest in advance mathematics (and who would blame you?, I don't), but I think that he should only tell that when you specifically ask for it, just don't mention it where others are with too (or in case if it's a private tutor, it doesn't matter). My general policy of these thing is "If they're not interested in it, and it's not mandatory, tell them they should (for now) forget about it, if they're interested in it (or become interested in it, who can tell), thell them how it works, it really helps when they decide to do something specifically in that area later on. Never ever say that it cannot work, unless of course, it cannot ever work. Ever."

I hope you accept my excuse, as as you said, I wasn't provided with enough information to know this one. I also hope you find my opinion agreeable, that would relieve a lot of stress from this thread. But then, we and agreeing... In this type of discussions that seems to be sort of a paradox
March 30th 2006, 04:58 PM
dragon.gif
You just don't seem to realise that the existence or rationality (your def) of something doesn't suddenly change when you call it a different way.

I don't think that it changes. In fact i think quite the reverse, ie that, like you said, "the existence or rationality (your def) of something doesn't suddenly change when you call it a different way". I don't know how you got the idea that I though otherwise.
March 30th 2006, 05:02 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
I've brought up a late addition (clearly marked as such), which might explain why I'm thinking that, sorry if I'm mistaken.

And if there's no difference, then we agree and I don't see the point of this (part of the) discussion.

Yay! We agree! It's possible! Let's have a cookie for this shall we? Or if you don't like cookies, we could celebrate it in another way
March 30th 2006, 05:05 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
I meant that after they have been proved they are useless.

No they aren't. Other people might want to think about why people thought that it was true, while it was false, which is also part of trying to evaluate the nature of reality/existence.

The part "not my brain gone wrong" indicates that you think I thought that.

I never said I didn't think you thought that. I just said I never said it.

Okay, that one was poor, and not to be taken seriously.

While you might not have directly said, nor meant to say, nor ever thought about the whole idea of ever saying, nor ever thought about the whole idea of thinking about my brain going wrong, it made that impact on me. You say complex numbers aren't rational (your def), I think there is a perfectly valid reason for them to exist. That's almost (not entirely) like saying I'm not rational, while I have yet to see any proof that they cannot exist. Of course there are no real numbers (math def) that, when squared, are -1. That's the whole point of complex numbers anyway: providing a facility we hadn't had yet. But saying I'm not rational is like saying my brain doesn't think rational. And imho (in my humble opinion), my brain is going wrong when it doesn't think rational.

And complex numbers are logical, just not in the system you've been taught. You nead to broaden your mind away from only accepting elementary algebra to be able to see the logic. Of course, only if you want. See my comment on your tutor somewhere else, which we have already discussed about.

As long as you accept that complex numbers can be logical in a logical system that you haven't been taught, I'm happy, as it's already better than a blunt "they're not logical" approach.

LATE ADDITION: I've already done a step towards you by accepting that in the math you've been taught complex numbers aren't logical. "math you've been taught" not meant as a negative term, although it might sound like one. It has helped me to see things from your point of view. I'm deep into advanced math everyday, so I sometimes lose track of that non-math people might not have heard of things like complex numbers. Or have heard of them, but don't know how to use them. Or in general don't use them how I do. I find it great that you know of complex numbers already, and that you know one of their uses (Solving x^2 + 1 = 0). I just forgot that most people don't see any way to fit this into real life, and put them aside as 'some freaky mathematical concept of which I don't see any way to fit it into real life'

I hope you accept my views as much as I accept your views. With your information and mathematical knowledge of the matter, your view is correct. With my information and mathematical knowledge of the matter, my view is correct.
March 31st 2006, 03:39 AM
fish.gif
Simeon
Peasant He/Him Netherlands
Any fool can use a computer. Many do. 
I'm glad that the computer science i will be doing won't require things like vectors, etc, because I have no intrest or need for them.

So did I when I had a quite mathematical course on these topics.. but now that I think of it, you'll need vectors and matrices for several things. If you think of a vector as an arrow in a plane then you'll need to know some operations on vectors to for example, calculate 3D graphics (and the coordinates of the system are stored in a matrix). The course on computer graphics is next year but that's what I've heard so it'll become useful then. Or, if you think of a vector as a bunch of numbers in a sequence, then it's basically an array In the assignment I'm doing now, the idea is to use a genetic algorithm to evolve the numbers in a vector which can be used for an artificial intelligence Reversi (Othello) program.. I admit, you don't need to know much about vectors there because you're just using an array in the code. But on the other hand, if you're a "computer scientist" (that word sounds so much better than the Dutch "informaticus" ), you should know what a vector or matrix is and preferably a little more than "a certain way to represent a group of numbers"
March 31st 2006, 10:41 AM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
A genetic algorithm that takes 11 days to calculate one vector. Or did you improve already?

Maybe I'm taking that AI course next year... Could be fun
March 31st 2006, 11:03 AM
fish.gif
Simeon
Peasant He/Him Netherlands
Any fool can use a computer. Many do. 
A genetic algorithm that takes 11 days to calculate one vector. Or did you improve already?

We improved it It was 11 days because the method that had to calculate the value of a square on the board relied on a try/catch construction which is nice but too slow when you call it millions of times. Basically the code needed the catching part too often but we won't do that in the future anymore (in time critical situations anyway). For those unfamiliar with try/catch, you basically "try" the code and "catch" an exception when it goes wrong (like divide by 0 or other exceptions). It kinda makes sense because (but this I don't know, it's just what I figured) when "trying" some code, you need a backup of the variables just before you start trying the code because when it goes wrong, you need to revert to those again.

We rewrote it and now the time has reduced to 1 - 3 secs for each game (and we need to play 18750 games). Because of this reduction, it takes something like 10 hours to evolve that vector with a search tree depth of 2 so it's likely that we're going to increase the depth of the search tree to get a better vector in the end. Now we're 'only' doing one of our own moves and one countermove by the opponent but of course, the deeper we can look in the tree, the better the decision will be
March 31st 2006, 11:13 AM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
From 11 days to 10 hours? Way to go
April 1st 2006, 12:56 PM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
@DraconicDink:
You find the complex numbers irrational, because you don't think it's logical to exist a number a, and a*a=-4.
Let me give you another examples. Let's say I move in your direction with the speed v1, and you move in my direction with the speed v2. It seems logical that an observer that stays on my head, sees you coming with the speed v=v1+v2(elementary physics).
Well the relativity theory, sais something else. Now, you're going to say that the relativity theory is irrational?
April 1st 2006, 01:38 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
I believe he already said so in a discussion before...
April 1st 2006, 04:09 PM
goblinm.gif
Here in the united states, it's hard just to take the national math olympiad (USAMO). I only got to take it my senior year of high school (I scored 13/42, which was bad.)
April 2nd 2006, 06:33 AM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
I remember that USA had Romanian math teacher, that trained you for the international faze: Titu Andreescu.
April 2nd 2006, 05:19 PM
dragon.gif
...calculate 3D graphics...

My programs won't even require me to do 2D graphics let alone 3d graphics so I'm quite safe in that respect.
April 2nd 2006, 05:38 PM
dragon.gif
No they aren't. Other people might want to think about why people thought that it was true, while it was false, which is also part of trying to evaluate the nature of reality/existence.

That's the same process starting again for a new person, hence a new case. I meant for incidual cases/people.

While you might not have directly said, nor meant to say, nor ever thought about the whole idea of ever saying, nor ever thought about the whole idea of thinking about my brain going wrong, it made that impact on me. You say complex numbers aren't rational (your def), I think there is a perfectly valid reason for them to exist. That's almost (not entirely) like saying I'm not rational, while I have yet to see any proof that they cannot exist. Of course there are no real numbers (math def) that, when squared, are -1. That's the whole point of complex numbers anyway: providing a facility we hadn't had yet. But saying I'm not rational is like saying my brain doesn't think rational. And imho (in my humble opinion), my brain is going wrong when it doesn't think rational.

No it is like saying that one thought of your is not rational, not that you as a whole are. And that comment is not derogative or like saying that your brain is going wrong, since even people like myself that value rational thinking so highly sometimes stuff things up and think irrationally. No one can think rationally all of the time. Also rational thinking is a choice thing that is not effected by brain ability, except in the worst cases of brain damage. It is a Mind thing. Note the distinction of the capital 'M', which even scientists use sometimes. By "choice thing" I mean that we choose to either think rationally or not to, though the choice may not be so blatant and may in fact be quite subtle.

And complex numbers are logical, just not in the system you've been taught. You nead to broaden your mind away from only accepting elementary algebra to be able to see the logic. Of course, only if you want. See my comment on your tutor somewhere else, which we have already discussed about.

Based on what I am taught? No. I never take someone else's opinions or statements on face value. I analyse them using reason and decide for myself if they have merit. So in other words, I form my own opinion.

As long as you accept that complex numbers can be logical in a logical system that you haven't been taught, I'm happy, as it's already better than a blunt "they're not logical" approach.

First I need evidence. I will not believe anything without evidence of some kind, be it the evidence that it stands up to rational thinking or the more typical sort of evidence.

I'm deep into advanced math everyday, so I sometimes lose track of that non-math people might not have heard of things like complex numbers.

Oh, I am a maths person. I'm just not a advanced maths person. I strugled alot with calculus and triginometry in high school. However, I excelled at algrebra and numbers (well normal ones anyway) and arithmetic.

'some freaky mathematical concept of which I don't see any way to fit it into real life'

Oh, I see that there is some real life use for them. it's just that the vast majority of people don't need them.
April 2nd 2006, 05:40 PM
dragon.gif
Well the relativity theory, sais something else. Now, you're going to say that the relativity theory is irrational?

Yes actually I do agree with the relatively theory, just not for the reason you seem to be implying.
April 2nd 2006, 05:40 PM
dragon.gif
I don't think NZ even has one.
April 2nd 2006, 06:16 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
That's the same process starting again for a new person, hence a new case. I meant for incidual cases/people.

Then tell what you mean. As you said it, it means that it didn't have any point in philosophy at all. It is true that for one specific person, it will become useless. Not for the whole of philosophy.

No it is like saying that one thought of your is not rational, not that you as a whole are. And that comment is not derogative or like saying that your brain is going wrong, since even people like myself that value rational thinking so highly sometimes stuff things up and think irrationally. No one can think rationally all of the time. Also rational thinking is a choice thing that is not effected by brain ability, except in the worst cases of brain damage. It is a Mind thing. Note the distinction of the capital 'M', which even scientists use sometimes. By "choice thing" I mean that we choose to either think rationally or not to, though the choice may not be so blatant and may in fact be quite subtle.

If I specifically say that specifically my brain is going wrong when I don't think rational, then it is still true in specifically my case. Of course, I could have said that while my brain was going wrong, which is probably the case. Thinking of the recursion that would give just makes my head explode.

Based on what I am taught? No. I never take someone else's opinions or statements on face value. I analyse them using reason and decide for myself if they have merit. So in other words, I form my own opinion.

Then it's still based on what you're taught. Even your own opinion is basen on what you're taught, as it uses it as input for a complex (har har, pun, in this context) evaluation process. Based on if the input makes sense or not (to you), you form your opinion.

First I need evidence. I will not believe anything without evidence of some kind, be it the evidence that it stands up to rational thinking or the more typical sort of evidence.

Evidence that it can be logical in another system is the "a+bi" -> (a,b) example I gave a few posts above. In short, you can use complex numbers to describe a place in a 2D plane. In that case "a+bi" just means something like "go a steps to the east, then b steps to the north". You don't even have to use i*i = -1, but if you do, you can use it for coördinate systems transformation. For example, instead of "go 2 steps to the east, then 2 steps to the north", you might say "when facing east, turn 45 degrees counter-clockwise, then go sqrt(8) steps forward".
I'm willing to teach you more about this particular use of complex numbers, as long as you know the concept of polar coördinates (when facing east, turn 'theta' degreas counter-clockwise, then go 'r' steps forward). And even when you don't know that, I think I've made the whole point about those clear with the thing between parentheses.

Oh, I am a maths person. I'm just not a advanced maths person. I strugled alot with calculus and triginometry in high school. However, I excelled at algrebra and numbers (well normal ones anyway) and arithmetic.

Nice. Interesting how your use of "normal" depends on "just not a advanced maths person". Being an advanced math person, more, for you "not normal", stuff, suddenly becomes normal. I guess we're agreeing that it sort of depends on how "normal" you find stuff, and for what systems you have use.

Also interesting is how my use of "non-math" depends on how an advanced math person I am.

Interesting, but trivial to the discussion, as we both agree, but we just post our things from a different point of view (pov, an "advanced math person" against a "not so advanced math person"), thus using the same words with different meanings, dependent on the pov, which causes confusion. I hope I've cleared things up

Oh, I see that there is some real life use for them. it's just that the vast majority of people don't need them.

In that we agree, though we use slightly different words At least, I know that what I mean is just what I think you mean by what you just posted. It might be that it has gone wrong with my interpretation of your post.

Last but not least, a round of nitpicking! Oh, the joy. Ignore me if you wish, as the sole purpose of what now follows is making a point (in the sense that it matters) of things that do not really matter in the discussion.

<nitpick>
Oh, I see that there is some real life use for them.

I believe "them" references to my "freaky mathematical concept" ('my' meant as in my quote, not as in 'my concept', as I have more), with which I (amongst other things) meant complex numbers. This contradicts "First I need evidence".

At least, if with that you meant you need evidence of the fact that "complex numbers can be logical in a logical system".

Since you see that there is some real life use for them, use that real life use you see as evidence.

You posted "Also I'm curious to see if you can come up with any examples at all let alone realistic ones.", with which you meant examples of complex numbers (do a search in this thread).

Same here, use that real life use you see as example.

Either you're not entirely consistent, or not completely saying what you really mean, assuming that I should be able to get it from context (in which case I have obviously failed), or you just use entirely different words, in ways that are totally unknown to me, or you're doing some more evil practice: Saying things first, then later sneaking out of it by saying "that's not what I meant". Truely evil, that one, as it renders a good discussion pointless.

I believe you are (generally, at least) a good person, so I'll just scratch the last possibility. The fact that I think of such things probably says more of me, than anything else

</nitpick>

You can safely stop ignoring here, as I'll try to make sense from now on.
April 2nd 2006, 06:38 PM
dragon.gif
Well since each person has to make their own philosophy, personal philosphy is all that intrests me not a so-called "collective philosphy", since in truth there is none since no two people's philosphy is the same.

ADDITION: I understand that you are adding more and am waiting patiently so that I can respond to or at least read it.
April 2nd 2006, 07:02 PM
wizard.gif
Chrispy
Peasant He/Him Canada
I'm a man, but I can change, if I have to.I guess. 
Relativty works for v = v1 + v2 if you consider each of those velocities to be energy vectors. You need to do some simple calculations to figure out what v is, but it's done easily enough in the end.
April 3rd 2006, 04:43 PM
sob_scorpb.gif
LadyValoveer
Peasant He/Him New Zealand
Mildly deranged. 
We do, if you're referring to a national math competition. I don't remember exactly what the exams are called, but I do remember they had the word 'Australian' in their title.

My English teacher sprung the creative writing one on me three hours before it was supposed to start. I got distinction, which is all right.
April 3rd 2006, 05:16 PM
dragon.gif
Evidence that it can be logical in another system is the "a+bi" -> (a,b) example I gave a few posts above. In short, you can use complex numbers to describe a place in a 2D plane. In that case "a+bi" just means something like "go a steps to the east, then b steps to the north". You don't even have to use i*i = -1, but if you do, you can use it for coördinate systems transformation. For example, instead of "go 2 steps to the east, then 2 steps to the north", you might say "when facing east, turn 45 degrees counter-clockwise, then go sqrt(8) steps forward".

I fail to see the logic in your argument.
April 3rd 2006, 05:19 PM
dragon.gif
We do, if you're referring to a national math competition. I don't remember exactly what the exams are called, but I do remember they had the word 'Australian' in their title.

Do we? First I've heard of it.

My English teacher sprung the creative writing one on me three hours before it was supposed to start. I got distinction, which is all right.

We have an a creative writing one? The only ones I know of aren't school related. And what do you mean by "distinction"?
April 3rd 2006, 06:28 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
Complex numbers are logical if you are in the system in which there's no multiplication, only addition. In that case, you can see a+b*i as (a,b), which means "Go 'a' steps to the east, and 'b' to the north". That's a logical explanation of a coördinate, relative to where you're standing now, which I've just called (0,0).

(a,b) + (c,d) = (a+c, b+d) is the normal way of changing
"Go 'a' steps to the east, and 'b' steps to the north." "That's it?" "Euhm... no, wait I forgot! Then you should take 'c' steps to the east and 'd' steps to the north"
into
"Go 'a+c' steps to the east, and 'b+d' steps to the north".

Not surprisingly, (a+b*i) + (c+d*i) = (a+b)+(c+d)*i. The part without i is still the first coördinate, the part with i is still the second coördinate. All fits.

In this way, complex numbers are a completely logical way of describing 2D-coördinates.

So then they are logical in another system, being 2D-coördinates. In the post you replied to, you can leave anything away after "You don't even have to use i*i = -1". Why use all properties when you don't have need for all of them?

Now, you could ask why one would possibly choose complex numbers above 'normal' 2D-coördinates. You could say it's a matter of preference. They can have added value, if you have the need for it. Hence the preference, those who have the need probably prefer complex numbers, those who don't, probably prefer 2D-coördinates (or maybe even the "steps-taking" description).

Since you probably don't have need for that added value, I won't bother to explain it. It isn't part of this discussion, anyway, as I've already shown that there is a system in which they are logical, which satisfies "Evidence that it can be logical in nother system", in which 'it' refers to 'the use of complex numbers'.

#end of my 'argument' in return here. Some non-discussion related stuff below:

When you said that you "strugled alot with calculus and triginometry in high school. However, I excelled at algrebra and numbers (well normal ones anyway) and arithmetic." I thought 'oy'.
While complex numbers are a purely algebraïcal concept (they are an instance of a common kind of ring, which is an abstract algebraïcal concept... Too difficult to explain in this post), calc and trig are the areas in which they're used most by (to my standard) less mathy persons.

In any case, I won't mind teaching you the added value (of coördinate transformation). In fact I'd be really happy to share my mathematical knowledge with anyone who asks for it, and really shows interest. Then, you can do with that knowledge what you want. Reject, accept, ignore, print out and use as toilet paper, share further, point a shotgun at it... whatever you want. Really, I don't care. I'd prefer if you share it with other people who are interested, but if you choose to do otherwise, it's fine with me.

Also, I've found this link on Eulers formula (e^(i*pi) = -1, and in general what e^xi is supposed to be). It might contain some useful insights on the use of complex numbers, although the initial question doesn't seem like it, the last post describes why complex numbers are useful in real-life. If you have the need for it:
http://mathforum.org/library/drmath/view/52251.html.

LATE ADDITION:

More questions in this archive might be interesting to read. To pick a few:
Uses of Imaginary numbers
Imaginary Numbers in Real Life
Defining Complex Numbers
Imaginary Numbers - History and Commentary
There are more in the archives of people who wondered how complex numbers could be possible, how to visualise them, what they are, etc. Kinda like what I'm trying to explain here, but then by people who have the ability to explain.
April 3rd 2006, 07:25 PM
wizard.gif
Chrispy
Peasant He/Him Canada
I'm a man, but I can change, if I have to.I guess. 
It may be easy enough to describe negative root numbers (imaginary is misleading) with algebra, but they have quite the bit of use in mid-level calculus. Past that, well, I'm not there yet. Fourier transformation ftw.
April 5th 2006, 02:31 PM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
The use of complex numbers in geometry:
You can express them in two ways:
The algebrical way: z=a+b*i.
The trygonometrical way: z=r*(cos(phi)+i*sin(phi))
Think this way: We have one point A(a,b). Sometimes, it's usefull to retain it's coordinates like this(for example, when we need to calculate distances). But, some other times, we need to retain polar coordinates: r-the distance from the origin. phi-the angle between OA and Ox, measured in trig way.
Here comes the multiplying and the division of complex numbers:
z1=r1*(cos(phi1)+i*sin(phi1))
z2=r2*(cos(phi2)+i*sin(phi2))
z1*z2=r1*r2*(cos(phi1+phi2)+i*sin(phi1+phi2))
z1/z2=(r1/r2)*(cos(phi1-phi2)+i*sin(phi1-phi2))
Now, let's find a good use for these: we have some nice formulas:
Let's consider three points: A(z1), B(z2), C(z3)
A, B and C are colinear if and only if arg((z1-z2)/(z2-z3))=0, where arg(z)=phi. Isn't this nice?
And there are a lot of formulas like this.
There are a lot of formulas even for the algebric form of complex numbers.
Let be eps a cube root of 1, that is not 1(in fact is a solution for the equation x^2+x+1=0).
A triangle ABC is echilateral if and only if z1+z2*eps+z3*eps^2=0.

In the end, I'll give you an example of a geometry problem that can be solved by complex numbers much more easy than using classical geometry:
Let be ABCDEF a hexagon. A1,A2,A3 are the middles of AB,CD and EF, while B1,B2,B3 are the middles of BC,DE and FA. Prove that A1A2A3 and B1B2B3 have the same center of mass(try it with and without complex numbers).
April 5th 2006, 03:36 PM
goblinm.gif
I didn't know Andreescu was Romanian, but yeah, I think he's still in charge of the US team.

How long did you have for those questions? USAMO is 8 hours for 6 questions, but the questions are definitely harder (or at least less conventional.)

EDIT: I can do questions 1, 3, and 4. My trick for 4 is, set:

h(x) = x * g(x)

Then for some a,b with a+b=1, h(x) = h(ax)+h(bx). This is an easier relation to deal with, although you still need the continuity of h(x)/x, of course.
April 5th 2006, 06:17 PM
dragon.gif
Sorry but I still don't understand what you're saying. However, please do not try to explain it again. I think you are referring to a level of mathematics above my current level of understainding. In my Bridging Mathematics and Statistics paper we are only just now getting to Equations I(functions of graphs with x and y coordinates).

And no I don't want you to try to teach me, but only because I do not currently have a good enough understanding of mathematics at that high a level.
April 5th 2006, 06:19 PM
dragon.gif
It may be easy enough to describe negative root numbers (imaginary is misleading) with algebra, but they have quite the bit of use in mid-level calculus. Past that, well, I'm not there yet. Fourier transformation ftw.

Yes, but most people don't have a need for mid-level calculus, it just doesn't help with anything they do, so to the vast majority of the population complex numbers are not at all useful.
April 5th 2006, 06:22 PM
dragon.gif
I wish I understood what you just said, cyrpy, but I understood only the english bits. The mathematics parts and the geometry parts were way above my level of mathematical understanding.
April 5th 2006, 06:55 PM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
Ahh, that explains a lot. Heh, for most of the math I'm trying to explain you'll have to have an idea about vectors and operations on vectors (like addition).

"Functions of graphs with x and y coordinates" sounds like f(x,y) = x+y, so that'll be a step forwards to understanding vectors. Good luck, or at least have fun
April 6th 2006, 01:20 AM
sob_scorpb.gif
LadyValoveer
Peasant He/Him New Zealand
Mildly deranged. 
@Draconic:

We have math, English, science and I'm not sure what else. The creative writing is a new one they created when I was about half-way through high school, which would make it about four/five years old.

The highest possible mark is 'high distinction', followed by 'distinction', 'merit', and 'participation'. I can't remember the percentage mark involved, which may be why I never sat the math one . If I stumble upon an old marking schedule I'll let you know.
April 6th 2006, 06:16 AM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
We had 3 hours. It wasn't that hard because it wasn't the national olympiad, it was just an inter-county contest.
I'll have the national olympiad on 17, this month.
For question 4, that was a nice observation, but did you managed to solve the problem using it?
For question 2, I'll tell you my ideea:
m=1: F is obviously surjective.
If m!=1, all we have to do is finding a matrix A that can't be equal with X^m, no mather what X is.
I think all the singular matrix have this property, but I'm not sure. For this question it's enough if we find one. So let's take A=((0,1),(0,0)).
I think it's elementary to prove that X^m=A has no solutions in M2(C).
April 6th 2006, 10:18 AM
custom_magicman.gif
magicman
Peasant They/Them Netherlands duck
Mmmm, pizza. 
My trick for 4 was actually integrating it:

G(x) = G(ax) + G(bx), where G(x) = \int g(x) dx

Still need the continuity of g here. I believe Riemann-integrals of (mostly everywhere) continuous functions are continuous also, because its derivative exists and is equal to the original function.

Other than the way we came there, it's the same situation

Btw, not all singular matrices do the job, for example:

((1,0),(0,0)) * ((1,0),(0,0)) = ((1,0),(0,0))
((0,0),(0,1)) * ((0,0),(0,1)) = ((0,0),(0,1))

These matrices serve as their own identity.

As for the third one... more analysis, but it seems an awful lot like the limit definition, which is needed for continuity. I didn't really look at it yet.
April 6th 2006, 02:27 PM
goblinm.gif
Three hours is quite fast, for those questions!

After I noticed:

h(x) = h(ax) + h(bx) ==>
either h(ax) < ah(x) and h(bx) > bh(x),
or h(ax) > ah(x) and h(bx) < bh(x)
or h(ax) = ah(x) and h(ax) = bh(x)

then it became obvious that:
g(x) = ag(ax) + bg(bx) ==>

either g(ax) < g(x) and g(bx) > g(x)
or g(ax) > g(x) and g(bx) < g(x)
or g(ax) = g(bx) = g(x).

From here we find (for positive x and y):
g(x) > g(y) for all y < x ==> g(ax) and g(bx) < g(x) for all suitable a,b, a contradiction by the above.
g(x) < g(y) for all y < x ==> g(ax) and g(bx) > g(x) for all suitable a,b, a contradiction (again) by the above.
Say we have positive x, y with g(x) < g(y). Let:
S={z > 0|g(z) >= g(y)}
Say Y=inf S and Y>0. Then we can find positive Y'<Y such that g(Y')>=g(Y)>=g(y), so that Y' is in S and Y'<Y, contrary to Y' being the inf (greatest lower bound) of S. Therefore inf S = 0. By a similar argument, if:
T={z > 0|g(z) <= g(x)}
then inf T = 0. Thus the function is discontinuous at 0, a contradiction.

Really, I didn't directly use the xg(x) thing in the proof, but I never would have figured out how to do the problem if I hadn't thought of it.
April 6th 2006, 04:00 PM
knightg.gif
cypry
Peasant He/Him Romania
Chop your own wood, and it will warm you twice. 
Silly me. I didn't meant to say singular matrix. I meant to say matrix A, that A^2=O2. Another example is ((-1,1),(-1,1)).
April 8th 2006, 04:29 AM
dragon.gif
"Functions of graphs with x and y coordinates" sounds like f(x,y) = x+y, so that'll be a step forwards to understanding vectors. Good luck, or at least have fun.

Not f(x,y) (not yet anyway). Just x=f(y) or y=f(x).
April 8th 2006, 04:37 AM
dragon.gif
Well Kaipara College never told us about them.
April 11th 2006, 01:16 PM
pq_water.gif
I'm sorry to drag this up again, but alas, I have been absent. Proving a thought erroneous does not make it useless, from a philosophical standpoint, to either an individual or people as a whole... in my humble opinion. Examining why any opinion, thought, belief or assumption was posed in the first place, erroneous or otherwise, is both within the realm of philosophy and enlightening (it reveals something about the original 'thinker' and his/her circumstances, personal history and, if you will, his/her 'reality'). The same goes for erroneous theories... such as Geoffrey of Monmouth's presumption that Stonehenge was moved to its current location thanks to the magic of Merlin... arguably its not the case, it didn't really happen that way... but it provides much insight as to 14th century society....
My rather long-winded point? Any thought, whether true or false, reasonable or unreasonable, justified or otherwise, has worth from a philosophical standpoint, simply because it was thought in the first place.
Before you argue again, please think about it without getting defensive.
Thanks.