On Dec 29, 2019, at 18:20, Chris Angelico <ros...@gmail.com> wrote: > > On Mon, Dec 30, 2019 at 11:47 AM Steven D'Aprano <st...@pearwood.info> wrote: >> >> On Mon, Dec 30, 2019 at 08:30:41AM +1100, Chris Angelico wrote: >> >>>> Especially since it fails quite a few commonsense tests for whether or >>>> not something is a number: >> [...] >>>> The answer in all four cases is No. If something doesn't quack like a >>>> duck, doesn't swim like a duck, and doesn't walk like a duck, and is >>>> explicitly called Not A Duck, would we insist that it's actually a duck? >>> >>> Be careful: This kind of logic and intuition doesn't always hold true >>> even for things that we actually DO call numbers. The counting numbers >>> follow logical intuition, but you can't count the number of spoons on >>> a table and get a result of "negative five" or "the square root of >>> two" or "3 + 2i". >> >> That's because none of those examples are counting numbers :-) >> >> My set of "commonsense tests" weren't intended to be an exhaustive or >> bulletproof set of tests for numberness. They were intended to be >> simple, obvious and useful tests: if it quacks, swims and walks like a >> duck, it's probably a duck. The silent Legless Burrowing Duck being a >> rare exception.[1] > > Exactly my point! Counting numbers follow logical intuition; but you > attested that you could use logical intuition to figure out if > something is a "number". Not a "counting number". Logical intuition > does NOT explain all the behaviours of non-counting numbers, and you > can't say "oh this is illogical ergo it's not a number". The logic of > logical intuition is illogical. :)
Counting numbers are intuitively numbers. So are measures. And yet, they’re different. Which one is the “one true numbers”? Who cares? Medieval mathematicians did spend thousands of pages trying to resolve that question, but it’s a lot more productive to just accept that the intuitive notion of “number” is vague and instead come up with systematic ways to define and compare and contrast and relate different algebras (not just those two). Are complex numbers numbers? Sure, if you want. Or no, if you prefer. But they’re still not real numbers, much less natural numbers. That’s obvious, and nearly useless. What you really want to know is which properties of the reals also hold of the complex numbers, and that’s a lot less obvious and a lot more useful. And the same is true for IEEE binary64. You can say they’re not numbers, or that they are, or that some of them are and some of them aren’t, but they’re not the rationals (or the reals or the affinely extended reals or a subalgebra of any of the above); what you really want to know is which properties of the rationals hold under what approximation regime for the IEEE binary64s. _______________________________________________ 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/6OMWP4HWHGH6ES2VD4HIWS4Y6KDFA3SA/ Code of Conduct: http://python.org/psf/codeofconduct/
