29 июн. 2015 г. · The principle of transfinite induction essentially says that, for a given formula P(x), if P(0) is true, and the truth of P(α) is preserved by ...

14 сент. 2012 г. · Transfinite induction is using this sort proof idea on arbitrary sets. You want to list all the element of an arbitrary set in a way so that you ...

17 окт. 2010 г. · The axiom of choice is needed to justify the existence of an infinite sequence consisting of arbitrary choices.

4 дек. 2015 г. · The proof of transfinite induction is a simple extension of the usual proof of induction (and equal to the proof of transfinite induction on sets).

17 июн. 2021 г. · Induction merely states uniqueness of subsets of a well-ordered set, not existence of any particular well-ordered sets.

14 февр. 2013 г. · Every infinite ordinal can be written uniquely as the sum of a limit ordinal and a finite ordinal. Proof. If α is limit then α=α+0; ...

16 июл. 2023 г. · Transfinite induction requires two ingredients: 1) order, because the main point of induction is statement n ⇒ statement n+1, and 2) a base case (eg n=0).

29 июн. 2015 г. · The small object argument is a very important technique based on transfinite induction allowing for the construction of approximations/ ...

20 сент. 2016 г. · Transfinite induction is a proof technique. Transfinite recursion, on the other hand, is a construction technique.

6 дек. 2014 г. · I seem to be confused about how transfinite induction is carried out. I have looked at several examples and they seem to follow a procedure consisting of ...