*PM : proof of principle of transfinite induction, id = 2704-- WP guess : proof of principle of transfinite induction-- Status:
22.
*PM : proof of principle of transfinite induction, id = 2704-- WP guess : proof of principle of transfinite induction-- Status:
23.
The standard definition proceeds via transfinite induction and the ordering ( a partial ordering of Kleene's \ mathcal { O } ) is defined simultaneously.
24.
This can be continued to transfinite ordinals by transfinite induction; the union of all the higher centers is called the "'hypercenter " '.
25.
The integrity of the construction of " V " by transfinite induction may be said to have then been established in Zermelo's 1930 paper.
26.
It turns out that this example is not very exciting, since provably for all ordinals ?, which can be shown, precisely, by transfinite induction.
27.
Using the full AC, one can well-order the formulas, and prove the uncountable case with the same argument as the countable one, except with transfinite induction.
28.
The " V " notation ( for the class of all sets ) was not used by von Neumann in his 1920s papers about ordinal numbers and transfinite induction.
29.
This form of induction, when applied to ordinals ( which form a well-ordered and hence well-founded class ), is called " transfinite induction ".
30.
It is straightforward to prove ( by transfinite induction ) that the order type of the natural order on the ordinals less than a given ordinal \ alpha is \ alpha itself.
