5 ms·
Yes. Trivially, uncountable infinities have to be larger than countable infinities do they not? The set of reals contains within it the set of integers for exa
by seanhunter 4y ago
Yes. Trivially, uncountable infinities have to be larger than countable infinities do they not? The set of reals contains within it the set of integers for example but also contains a bunch of other stuff. (Not a mathematician obviously).
- schoen 4y agoThat argument turns out not to be enough! A counterexample is the set of rational numbers, which has the same cardinality as the natural numbers, even though the naturals are a proper subset of the rationals. Some infinite sets can be put into one-to-one correspondence with some of their proper subsets!