Andrew Barnert via Python-ideas writes: > People often think “well, natural numbers aren’t closed over > subtraction, so we’ll just always use integers, and integers aren’t > closed over division so we’ll just always use rationals, …” > assuming that if you keep following that you get to the one true > “numbers” somewhere around complex or quarternion. [...] But in > fact at each step you lose features as well as gain them. For the > most obvious example, while complex numbers give you closed > exponentiation, they take away ordering. So, they’re all useful for > different purposes.
This is the central point. The rules that you can use to calculate (or prove things) depend on which definition of "number" you use (this is precisely where category theory places its emphasis). I would choose a different example, myself: when you move from the integers to the reals, you lose the notion of "next". This lack makes explaining some properties of dynamic models based on differential equations a real PITA if you are teaching students who haven't already internalized the mathematics of continuous time dynamics. Can't blame them, really, it confused Zeno, too. :-) _______________________________________________ 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/FLXUNBD6HO5QWPVJ73CU7PK3IOMQIMZH/ Code of Conduct: http://python.org/psf/codeofconduct/
