On Oct 14, 2019, at 06:07, Steven D'Aprano <st...@pearwood.info> wrote: > >> On Mon, Oct 14, 2019 at 12:54:13AM -0700, Andrew Barnert via Python-ideas >> wrote: >>> On Oct 13, 2019, at 22:54, Chris Angelico <ros...@gmail.com> wrote: >>> >>> Mathematically, what's the difference between '1' and '1+0j' (or >>> '1+0i')? >> >> The details depend on what foundations you use, but let’s go with the >> most common construction. > > More importantly, the details depend on where you sit on the > Practicality vs Purity axis.
Well, sure. And in fact that axis is a different axis when working in different fields of mathematics. Type theory is a lot closer to foundations stuff than most areas of math are, and so is large-cardinal set theory, but they’re close in different ways from each other, and require different bits from it. > Mathematicians don't typically talk about "duck-typing", but if they > did, they'd be saying that the Integers quack like a subset of the Reals > no matter what those weird guys who care about foundational issues say Sure, but if you asked them “is it mathematically correct that integers are a subset of the reals, or that they aren’t?” their answer is usually going to be “Who cares?” Normally that isn’t a useful question, so it doesn’t need an answer. If you really need to know the rigorous answer (maybe you need it for your work, but much more likely it’s because, say, your nephew, who’s taking undergrad math courses, is asking…), you’d defer to people who care about that stuff, and give an answer based on the foundations. But in most fields you can go your entire career without ever needing to think about it. (At least once you pass and forget the relevant class late in your undergrad studies.) And of course that’s even more true for people doing mathematical physics or econ or programming theory or something. They probably didn’t even take that undergrad class to forget it later, and might not even know who to ask if the question came up. But because the question isn’t going to come up, it doesn’t matter. _______________________________________________ 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/MMMOW7IO2HUZMS7NZ5I2XWGRI3INANZZ/ Code of Conduct: http://python.org/psf/codeofconduct/
