Is infinity more than 6000?

[Pogle]

transfinite cardinals? Are they the ones who dress up as choir boys?

Naw they're just really BIG ones

[swamp]

transfinite cardinals? Are they the ones who dress up as choir boys?

Only in the Von Neumann universe.

It's all explained here.

[bogeyman]

Don't go there. Everyone who does ends up in an asylum: Cantor, Godel et . al.

Godel didn't end up in an asylum even though he was as mad as a bat.

He starved himself to death because he was afraid of being poisoned.

Poor old Kurt.

[sasguru]

Godel didn't end up in an asylum even though he was as mad as a bat.

He starved himself to death because he was afraid of being poisoned.

Poor old Kurt.

Ah yes that's true. But it was thoughts of infinity that dunnit.

[NotAllThere]

You guys are just 'aving aleph

[ASB]

You guys are just 'aving aleph

[threaded]

I think all the various forms of 'infinity' are just a bit of lazy thinking. It's not a number so why bother with it in mathematics?

Unless you can 'build' whatever it is you're building in a finite time then it will never exist, so it has no real meaning.

I always feel a proof that avoids invoking infinities has more substance. I mean these proofs where they say something doesn't exist, and then by invoking 'infinity' generate a contradiction, they just 'taste' wrong.

[bogeyman]

I think all the various forms of 'infinity' are just a bit of lazy thinking. It's not a number so why bother with it in mathematics?

Unless you can 'build' whatever it is you're building in a finite time then it will never exist, so it has no real meaning.

I always feel a proof that avoids invoking infinities has more substance. I mean these proofs where they say something doesn't exist, and then by invoking 'infinity' generate a contradiction, they just 'taste' wrong.

Clearly there are conceptual infinities, but probably not practical ones.

The number of numbers is infinite, but that is merely a concept, not an actuality.

The number of, say, atoms in the universe, while a very, very big number, is (probably) finite at any given point in time. The universe is itself (probably) finite.

Infinity is merely a mathematical device.

[EternalOptimist]

Clearly there are conceptual infinities, but probably not practical ones.

The number of numbers is infinite, but that is merely a concept, not an actuality.

The number of, say, atoms in the universe, while a very, very big number, is (probably) finite at any given point in time. The universe is itself (probably) finite.

Infinity is merely a mathematical device.

as a concept, is it of any use ?

[bogeyman]

as a concept, is it of any use ?

It prevents mathematics from falling apart at the edges. Otherwise, no, not really.