How Can I deduce from Cantor's Theorem that for every cardinal $\alpha$ there is a cardinal $\beta> \alpha$.
A cardinal is an ordinal which is equal to its cardinality.
2026-04-06 18:18:32.1775499512
Using only the def., how to show that for every cardinal there is a bigger one
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HINT: Note that by Cantor's theorem there is no surjection from $\alpha$ onto $\mathcal P(\alpha)$. Let $\beta=|\mathcal P(\alpha)|$, then $\alpha<\beta$.