ex-xian

We don't have to count something to know that it's infinite. To show that a set being finite leads to a contradiction is enough, as is the case with the proof of the infinitude of primes.

And then again, it might not be! If you have a legit challenge, then post it. Don't just make assertions.

So if a tree falls in the forest and there's no one there to hear it does it make a sound?

eh

Oddly enough, cosmologists would say even an infinite universe can expand. One explantion is here: http://itss.raytheon.com/cafe/qadir/q2457.html

Big Spoon

Regarding Cantor's set theory, his results are perfectly valid, the proof is inspirational and the end product is totally counter-intuitive, which in my opinion makes for brilliant mathematics. Far from a cancer!

Witt, do you not believe that mathematics is true independant of human perception?

Witt

Big Spoon:
Regarding Cantor's set theory, his results are perfectly valid, the proof is inspirational and the end product is totally counter-intuitive, which in my opinion makes for brilliant mathematics. Far from a cancer!

Agreed, except for the perfecty valid part.
Both Frege and Cantor assumed that every predicate has a class, and Russell showed that that is false.

i.e. EyAx((x e y) <-> Fx) is invalid.
The naive 'axiom of comprehension' fails for the Russell class.
i.e. ~EyAx((x e y) <-> ~(x e x)) is a theorem.

"Witt, do you not believe that mathematics is true independant of human perception?"

Yes, truth exists only within minds. Truth is dependent on conceptions of mind.

That '2+2=4' is true, requires mental understanding of the symbols and their presumed relations.

Without mind, 2+2=4, has no meaning at all.
There is no place in the world where we could find the number two.

There is no truth in the world, we interpret factual truth from existent states of affairs.

Witt