On Mon, Dec 30, 2019 at 5:48 AM Steven D'Aprano <st...@pearwood.info> wrote: > > On Sat, Dec 28, 2019 at 09:20:49PM -0800, Brendan Barnwell wrote: > > > The things that > > computers work with are floats, and NaN is a float, so in any relevant > > sense it is a number; it is an instance of a numerical type. > > You seem to be assuming that `x is an instance of type float (or > Decimal)` implies `x is a number`. That seems reasonable in the general > case (e.g. we would rightly expect that every instance of a type "Car" > represents an actual car) but in the specific case of floats (and > Decimal) the assumption breaks down. > > The writers of the IEEE-754 standard didn't choose the name "Not A > Number" at random. The name tells you their intention: NANs represent > values or quantities which are not numbers. It seems particularly > perverse to insist that even when a value is explicitly described as Not > A Number, it's actually a number. > > Especially since it fails quite a few commonsense tests for whether or > not something is a number: > > - Do NANs appear anywhere on the real number line or complex plane? > > - Can we successfully measure (say) the length of a piece of string > and get a result of NAN inches? > > - Can we successfully count the number of (say) spoons on a table > and get a result of NAN? > > - Do NANs obey, even approximately, the usual properties of numbers? > > 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". Extending the concept of "numbers" to include zero, negatives, laterals (complexes), etc is something that various different cultures had to come to terms with. (The ancient Romans, for instance, didn't have any way to represent zero - which means it was extremely difficult for their C programs to indicate successful termination. This led directly to the empire's downfall.) More useful would be to look at the useful operations and invariants that can be maintained, but that doesn't work too well for finite subsets of numbers. Very few operations are closed for, say, "sixteen bit integers". Nor for "rational numbers with denominators that are powers of two between -1024 and 1024". There is no easy way to define "number" in a way that is both mathematically pure AND practically useful. ChrisA _______________________________________________ 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/O5ODZ2D2W43DSGQMW76OQW65KWLAVEXO/ Code of Conduct: http://python.org/psf/codeofconduct/
