On Monday, April 1, 2013 5:01:04 AM UTC-7, Jesse F. Hughes wrote:
> david petry <email@example.com> writes:
> > Applied mathematicians know they have to produce something that is > > of use to the scientists, which does imply that they are taking > > falsifiability into consideration.
> I still don't understand.
That doesn't surprise me.
> Can you give an example of some piece of mathematics that an applied > mathematician would choose to avoid, because it's not "falsifiable"?
Cantorian set theory.
> And can you tell me whether the axioms of, say, the theory of real > numbers are falsifiable?
I don't know what you are referring to by "the axioms of the theory of real numbers".
> Of course, if the theory of real numbers is not falsifiable, it would > seem you have a problem, right? Don't applied mathematicians (and > scientists!) use that theory regularly?
The real numbers can be developed in the context of falsifiability, which should be obvious since scientists use real numbers.
The real numbers that scientists use are finite precision real numbers, which can be thought of as rational numbers together with an error estimate. The theory of infinite precision real numbers can be developed as the limiting case when the error goes to zero.