[tambourine_man]

It's only a proof if you take a leap of faith and accept certain things. You could argue that that's how math works, but to me the less axioms we need, the better.

I really love this quote from Wittgenstein:

"Where the nonsense starts is with our habit of thinking of a large number as closer to infinity than a small one".

http://en.wikipedia.org/wiki/Controversy_over_Cantor%27s_the...

[pavel_lishin]

Which assumptions do you find troubling?

[tambourine_man]

That although both are infinite, there are actually more of one than the other.

That's treating infinite as if it's a limit, when it's not.

If it's uncountable and unmeasurable, than it's non hierarchical.

[pavel_lishin]

> That although both are infinite, there are actually more of one than the other.

That's not the assumption, that's the result.

[tambourine_man]

You're right. The assumption would be that there's a countability difference between Naturals and Reals.

That Naturals are infinite but countable and Reals infinite and uncountable.