Reply to Re: I gave up to the Computers National Olympiad
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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.
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.
