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 <miguelim...@yandex.ru> 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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