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 …

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 …

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 …

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 …

Apr 9, 2022 · Transfinite Construction, an intuitive interpretation. Ask Question Asked 3 years, 7 months ago Modified 3 years, 7 months ago

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 …

@PeteL.Clark The whole thing is interesting, but in his first example — showing a continuous function on [0,1] is bounded — is remarkably similar to your real induction, except written in …

The wikipedia page on the cardinal numbers says that $\\aleph_0$, the cardinality of the set of natural numbers, is the smallest transfinite number. It doesn't provide a proof. Similarly, this …

Oct 1, 2013 · Transfinite Sets & The Countability of The Primes. Ask Question Asked 12 years, 2 months ago Modified 12 years, 2 months ago