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C (complex numbers) is a field, just like R (real numbers). It's an algebraically closed field, unlike R, so in some sense it's actually the most natural set to
by mr_pink 10y ago
C (complex numbers) is a field, just like R (real numbers). It's an algebraically closed field, unlike R, so in some sense it's actually the most natural set to call "numbers".
https://en.wikipedia.org/wiki/Algebraically_closed_field https://en.wikipedia.org/wiki/Algebraically_closed_field
- k__ 10y agoI'm not trying to argue for R being more a set than C. In my head a one dimensional thing like R is fundamentally different from a multidimensional thing like C.
- mr_pink 10y agoWell I was answering the question about why is C considered numbers - it's a field, hence elements of C behave exactly like numbers. Moreover, it's an 'algebraic closure' of R, hence a more natural choice for "all numbers", and it's a maximal one at that (i.e. quaternions and such are no longer fields and don't really behave like numbers, while C still does). Edit: FWIW, I consider the terminology of 'real' vs 'imaginary' completely stupid and misleading. This terminology didn't really make it to other languages, e.g. in Russian it's 'material' vs 'complex' numbers, but they don't use the term 'imaginary'.