Cantor normal form: Difference between revisions
m
no edit summary
No edit summary |
CreeperBomb (talk | contribs) mNo edit summary |
||
| (One intermediate revision by one other user not shown) | |||
Line 1:
{{stub}}
'''Cantor normal form''' is a standard form of writing ordinals. Cantor's normal form theorem states that every ordinal \( \alpha \) can be written uniquely as \( \omega^{\beta_1} + \omega^{\beta_2} + \dots + \omega^{\beta_k} \), where \( \beta_1 \ge \beta_2 \ge \dots \ge \beta_k \) and \( k \ge 0 \) is an integer.
When \( \alpha \) is smaller than [[Epsilon numbers|\( \varepsilon_0 \)]], the exponents \( \beta_1 \) through \( \beta_k \) are all strictly smaller than \( \alpha \). Thus, Cantor normal form can be iterated to form
| |||