
No, they aren't. They are polynomials in one variable "i" modulo i^2+1. Seriously, if you say complex numbers are just pairs of real numbers - you have to agree that double numbers (sorry, don't know the exact English term), defined by (a,b)+(c,d) = (a+c,b+d) (a,b)(c,d) = (ac, ad+bc) are just pairs of real numbers too. After that, you have two choices: a) admit that complex numbers and double numbers are the same - and most mathematicians would agree they aren't - or b) admit that the relation "be the same" is not transitive - which is simply bizarre. Lennart Augustsson wrote:
But complex numbers are just pairs of numbers. So pairs of numbers can obviously be numbers then.
On Mon, Oct 5, 2009 at 4:40 PM, Miguel Mitrofanov
wrote: Lennart Augustsson wrote:
And what is a number? Can't say. You know, it's kinda funny to ask a biologist what it means to be alive.
Are complex numbers numbers? Beyond any reasonable doubt. Just like you and me are most certainly alive.
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