Jun 6, 2020 · Transfinite is good when there is a notion of order, so "transfinite ordinal", or when you want to talk about non-standard real numbers which are larger than all the standard …

Jun 30, 2015 · Any "Principle" of transfinite induction can only be simply a statement of an extension of the standard 'one good turn deserves another' principle, a re-iteration of Cantor's …

Sep 21, 2016 · I'm trying to understand the concept of transfinite recursion. Can someone provide me examples which clearly illustrates transfinite recursion or provide some references which I …

Apr 9, 2022 · Transfinite Construction, an intuitive interpretation. Ask Question Asked 3 years, 9 months ago Modified 3 years, 8 months ago

The transfinite induction argument simply says something like induction, only general: suppose that you walked over all ordinals until $\alpha$, how do you plan on stepping through …

Shouldn't transfinite induction suffice to prove the axiom of choice for any system of sets indexed by a well-ordered set? I am reading Jech right now, but my knowledge of ordinals and …

Jul 16, 2023 · Could you please help me to know why transfinite induction only works on well-ordered set and not arbitrary set ? Why the fact that every susbset has a least element is …

Jun 30, 2015 · Learning transfinite induction, and the theory of ordinals, is a bit time consuming. Many mathematicians are perfectly fine by learning this simple one lemma, and avoiding to …

Jan 3, 2025 · So, you can essentially take a big transfinite ordinal like $\epsilon_0$ or $\omega_1$ or even a large cardinal and "fill it in" to get a continuum. This set is connected …

Apr 30, 2024 · I've been curious about transfinite number systems including infinite ordinals, hyperreals, and surreal numbers. The hyperreals in particular seem particularly appealing for …