On Wednesday, February 12, 2014 3:37:04 PM UTC+5:30, Ben Finney wrote: > Chris Angelico writes:
> > On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney wrote: > > > So, if I understand you right, you want to say that you've not found > > > a computer that works with the *complete* set of real numbers. Yes? > > Correct. [...] My point is that computers *do not* work with real > > numbers, but only ever with some subset thereof [...] > You've done it again: by saying that "computers *do not* work with real > numbers", that if I find a real number - e.g. the number 4 - your > position is that, since it's a real number, computers don't work with > that number. There is a convention in logic called the implicit universal quantifier convention: when a bald unqualified reference is in a statement it means it is universally quantified. eg "A triangle is a polygon with 3 sides" really means "ALL polygons with 3 sides are triangles" ie the ALL is implied Now when for-all is inverted by de Morgan it becomes "for-some not..." So "computers work with real numbers" really means "computers work with all real numbers" and that is not true > That's why I think you need to be clear that your point isn't "computers > don't work with real numbers", but rather "computers work only with a > limited subset of real numbers". Yes both these statements are true by above. In fact computers cannot work with real numbers because the real number set is undecidable/uncomputable. In particular, trivial operations like equality on reals -- IN GENERAL -- is undecidable. -- https://mail.python.org/mailman/listinfo/python-list