He was kind of caught between worlds here, because the other mathematicians -- most of whom weren't particularly devout -- often thought of his work as a weird waste of time, while the Church didn't understand what he was talking about and thought it sounded like witchcraft
-
-
I don't think we're quite on the same page - Cantor was the first to prove that not all infinities have the same size, which is what I meant by "infinite" as a definite quantity. But instead you only get an infinite tower of ever-greater infinities.
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
Aleph-null, the first infinite cardinal number (the size of the set of all natural numbers), actually does do all the paradoxical stuff people think of "infinity" doing It stays the same size if you add 1 to it, if you multiply it by 2, if you square it, etc
-
Hence you can't, in fact, usefully use it as "the biggest number" in normal math problems, you immediately run into contradictions
- Show replies
New conversation -
-
-
Well - a number that you can do math with. I'm not sure that qualifies as a 'definite quantity' though.
-
I'd certainly regard alelph 0 as a definite quantity as I meant it. My point is just that, as you climb up the power set hierarchy, you get greater quantities but - of course - all of them are infinite. So there is not just one single quantity "infinite".
- Show replies
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.