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 that sort of thing.)
Compared to the uncountable infinities, countable infinity is much more comprehensible, although it is still true that you cannot answer every question about it. And even if the universe continues forever, we are still talking about a countable sort of 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 that sort of thing.)
Compared to the uncountable infinities, countable infinity is much more comprehensible, although it is still true that you cannot answer every question about it. And even if the universe continues forever, we are still talking about a countable sort of infinity.