There's more than one countable infinity?
Somewhere in this thread there's been a mix-up between countable and uncountable.
There's only one countable infinity (at least if you're talking about cardinal numbers), and it's much more fun than the uncountable infinities (if by ‘fun’ you mean what is easy to understand). As Sniffnoy correctly states, there are many, many uncountable infinities, in fact too many to be numbered even by an uncountable infinity! (In the math biz, we say that the uncountable infinities form a ‘proper class’. Proper classes are related to Russell's Paradox, if you like th...
This is our monthly thread for collecting arbitrarily contrived scenarios in which somebody gets tortured for 3^^^^^3 years, or an infinite number of people experience an infinite amount of sorrow, or a baby gets eaten by a shark, etc. and which might be handy to link to in one of our discussions. As everyone knows, this is the most rational and non-obnoxious way to think about incentives and disincentives.