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