2 ms·
You need to consider the term “bijection” and what it means in practice. If I create a bijection of integers to integers f(x)=2x you can see that each member of
by opportune 4y ago
You need to consider the term “bijection” and what it means in practice. If I create a bijection of integers to integers f(x)=2x you can see that each member of the right side had exactly one member on the right, and vice versa, despite the left side containing some elements not on the right. There is no such bijection between ints and reals (by cantors theorem), but there is clearly a surjection of reals to ints (round down), so reals are of a larger infinite size.
I think a layman could easily understand this personally, without fancy math terms like bijection or surjection, the main exception being Cantors Theorem which fortunately has a plethora of nice visual proofs.
Anyway, the article is not really even about that but about potentially modifying ZFC to accommodate a particular outcome of the CH. I am quite interested in mathematics but to me this is a pointless philosophical argument because there don’t seem to be any useful or empirically verifiable results that depend on CH. Discussing CH to me seems to be more of a way for set theorists to troll each other and trigger cranks.