There’s more to mathematics than rigour and proofs (2007)

Re:There’s more to mathematics than rigour and proofs (2007) by shkkmo on Wednesday April 20, 2022 @01:18AM (#31093088)

I've been thinking about the reals a lot...beyond the rationals are all the real numbers like pi that have finite definitions, (even if those definitions, like pi's, require infinite computation.)

But there is also this vast set of reals that are simply undefineable, non-repeating sequences. These numbers are unmentionable and unknowable. Does it really even make sense to say that this subset of the reals exists in the same way that definable numbers do?

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Re:There’s more to mathematics than rigour and proofs (2007) by l33t2328 on Wednesday April 20, 2022 @01:25AM (#31093150)

Yes, of course. Because definable (really, computable) numbers don’t really “exist” either.

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Re:There’s more to mathematics than rigour and proofs (2007) by shkkmo on Wednesday April 20, 2022 @09:51AM (#31096950)

We can can use definable numbers. Pi is used with such massive frequency that is seems silly to say it has the same nonexistence as numbers that we can literally never even mention, let alone use.

My assertion is that there is something wonky with these u definable numbers and that wonkiness is directly related to how absolutely massive the infinity of reals is.

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