On Thursday, July 11, 2013 10:35:42 AM UTC-7, Julio Di Egidio wrote: > "Virgil" <email@example.com> wrote in message > > news:virgil-2828F2.14423709072013@BIGNEWS.USENETMONSTER.COM... > > > In article <firstname.lastname@example.org>, > > > "Julio Di Egidio" <email@example.com> wrote: > > >> "Virgil" <firstname.lastname@example.org> wrote in message > > >> news:virgil-BD8D66.13090609072013@BIGNEWS.USENETMONSTER.COM... > > >> > In article <email@example.com>, > > >> > firstname.lastname@example.org wrote: > > >> > > >> >> I deleted your formalism because it is meaningless. It cannot > > >> >> remove the fact that the urn is never empty of "the successor" > > >> >> which is always present - in infinity. > > >> > > > >> > Every natural that has successor is removed. > > >> > > >> Wrong: every one is removed but never all. Indeed (mind the > > >> spoiler): > > > > > > If you agree that every one is removed then you are agreeing that every > > > one is removed despite you denial of it. > > > > Speak for yourself, the one in denial here is you. Not only your statement > > is patently illogical for anybody able to think, I have even explained it > > formally, how your paralogism is just word salad. Here it is: > > > > >> To the paralogism that pretends to justify your take: 'for every ball > > >> n in N, exists step m in N such that n is removed at step m' just > > >> does *not* entail that 'the vase ends up empty', however you may > > >> think of formalising the problem and conclusion. > > > > > > When one adds that every one is removed before noon, one is equally > > > justified in saying the are all removed before noon. > > > > Every one *singularly* is removed at some specific time, but never *all*: > > i.e. that "everyone is removed by noon" meaning that all are removed is > > patently false logic. Of course, you will just keep repeating the same word > > salad ad nauseam: no surprise, as you are just WM's alter ego... > > > > >> Indeed, contrary to your pseudo-logic, for every step where 1 ball is > > >> removed, 2 (or more) balls are added, so that the vase rather must > > >> end up 'ever more full'. In fact, the set of balls that end up in of > > >> the vase, and the set of balls that end up out of the vase, both have > > >> cardinality aleph_0, with the needed bijections easily built. > > > > > > If you claim that some balls have not been removed before noon, name one! > > > And since every non-empty set of naturals has a smallest of first > > > member, you should be able to name the first one if there really were > > > one. > > > > > > So can you? > > > > Nope, and I have explained how that is: cardinality is based on bijections. > > If you want indexes, I'll use ordinals... > > > > Any serious objections? Of course not. >
Just a request for clarification.
Explain the differences, as far as properties, between the set of all Finite Cardinals and the set of all Finite Ordinals.