# ordinals

1. ### Having Sum Fun Counting Ordinals

This is a draft. Knowing me, it is probably nonsensical and filled with errors. I'm trying to enumerate some very large countable ordinal assuming of course that math isn't broken and I can't enumerate $\omega_1$ itself. ... And no, jic, I don't think math is broken. Why? Do you? :spin...
2. ### Ordinals

Hi, I'm trying to figure out what ordinal numbers are good for, or where they are used. Unfortunately I can only find definitions on how they are constructed etc. So am I correct that ordinals are just an "abstraction" for the ordering of well ordered sets and that there is an representative...
3. ### Relationship between P(N) and the countable ordinals

Does anyone know what Cantor considered the connection between the cartable ordinals (the second number class) and the power set of the natural numbers?
4. ### examples, sequences of ordinals

Give examples of strictly increasing sequences of ordinals such that \text{lim}_n(\alpha_n + \beta) \not = \text{lim}_n \alpha_n + \beta, \text{lim}_n(\alpha_n + \beta_n) \not = \text{lim}_n \alpha_n + \text{lim}_n \beta_n. I cannot think any examples that work for this one. The problem is...