On Mon, 14 Oct 2019 at 05:47, Andrew Barnert via Python-ideas <python-ideas@python.org> wrote: > > `1 in complex` is _not_ mathematically true. Simplifying a bit, the elements > of the algebra of complex numbers are ordered pairs of real numbers, and `1` > is not a pair. When you’re working in, say, complex analysis, you just assume > the usual morphism that maps every real to a unique complex (and some > complexes to a unique real), and you can loosely multiply a real by a complex > and so on.
This all just depends on your definitions. You can see some discussion of the approach taken in metamath here: http://us.metamath.org/mpegif/mmset.html#trivia """ One of the reasons that the proof of 2 + 2 = 4 is so long is that 2 and 4 are complex numbers—i.e. we are really proving (2+0i) + (2+0i) = (4+0i)—and these have a complicated construction (see the Axioms for Complex Numbers) but provide the most flexibility for the arithmetic in our set.mm database """ I guess the authors decided it was too painful to have 1 not be a complex number so they decided instead to define the integers as a subset of the complex numbers. Nothing wrong with that, just a different definition. The integers as a subset of the complex numbers still satisfy all the same properties. Oscar _______________________________________________ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/ITA5PEUBSCY3WW543XXKINIVZ7C2A7BD/ Code of Conduct: http://python.org/psf/codeofconduct/
