3 ms·
unrelated: how do we know there are no alephs between 0 and 1?
by keymone 5y ago
unrelated: how do we know there are no alephs between 0 and 1?
- Sharlin 5y agoIf you assume Axiom of Choice, you can define cardinalities in terms of ordinal numbers (an extension of naturals that generalizes the notion of "counting", or "indexing"). And ordinal numbers are well-ordered, ie. every element has a unique "successor" element.
- elcomet 5y agoThat's the definition of aleph-1. The continuum hypothesis is that 2^aleph-0 (number of sets of integers or number of reals) = aleph-1.