| 11. | Hilbert adopted and warmly defended Georg Cantor's set theory and transfinite numbers.
|
| 12. | The uniqueness of the sequence satisfying these properties can be proved using transfinite induction.
|
| 13. | This is again a definition by transfinite recursion.
|
| 14. | Like " oh, you study infinite-dimensional hyperchaotic transfinite differential matrix supermanifolds?
|
| 15. | This distinction is important, because many definitions by transfinite induction rely upon it.
|
| 16. | In group theory, Hamkins proved that every group has a terminating transfinite automorphism tower.
|
| 17. | This is important because it makes every set susceptible to the powerful technique of transfinite induction.
|
| 18. | One may continue into the transfinite.
|
| 19. | ? 1 1-CA 0 is stronger than arithmetical transfinite recursion and is fully impredicative.
|
| 20. | We create a counterexample by transfinite induction on the set of strategies under this well ordering:
|