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