4 ms·
Has anyone seen a formal proof of different cardinals based on axiomatic set theory? The diagonal argument in particular is very weak imo.
by jujulet 8y ago
Has anyone seen a formal proof of different cardinals based on axiomatic set theory? The diagonal argument in particular is very weak imo.
- dwheeler 8y agoI'm not certain how to interpret what you're asking. However, if what you're asking is how to derive numbers from basic axiomatic set theory, that is certainly available in metamath. An easy to read introduction is here: http://us.metamath.org/mpegif/mmcomplex.html http://us.metamath.org/mpegif/mmcomplex.html
- digama0 8y agoIt sounds like you are talking about Cantor's theorem, and its proof is here -> http://us.metamath.org/mpeuni/canth.html http://us.metamath.org/mpeuni/canth.html . The formalization is both short and straightforward, so while you might argue that the axioms of set theory aren't intuitive enough, the fact that they come together to prove the impossibility of bijection between a set and its powerset is unassailable.