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:
