"Zuhair" <email@example.com> wrote in message news:firstname.lastname@example.org... > On Nov 16, 11:36 am, "LudovicoVan" <ju...@diegidio.name> wrote: >> "Zuhair" <zaljo...@gmail.com> wrote in message >> news:email@example.com... >> >> > We still can characterize Cardinality in this setting. >> >> And you keep missing the point, as the various objections of course >> involve >> that the standard definition of cardinality for infinite sets is wrong! >> >> > So Cantor's diagonal is applicable to potential infinity context! >> >> Cantor's arguments are *only* applied to potentially infinite sets, in >> fact >> in standard set theory there is no such thing as actual infinity at all. >> >> Please get your head out of your ass and read and try to understand what >> you >> are rebutting before you actually get to do it. > > Good advice for you actually, since you don't know what you are > speaking about. So just try to read what is written here, and if you > don't understand what is written, or you have some problem with it, > then just try to ask politely about it, so that I or others who are > more informed that you can explain matters to you. Anyhow standard set > theory "ZFC" is of course not limiting itself to the potential > scenario, not even to the one I've presented here, that's why it > accepts Impredicative definitions, as well as non well founded > versions of it, the reason is that it doesn't have a problem with > considering the possibility that all sets in the universe of discourse > are GIVEN beforehand, and Godel's have stated that there is nothing > wrong with this assumption, so there is no problem with considering > that the set N is already Given, i.e. it is there beforehand with all > its elements, i.e. N is a completed actual infinite set, in standard > set theory understanding of N is not limited to the potential of > becoming that I've presented here. However here I showed that even if > we assume potential infinity in the sense I've presented, which is as > I showed here the most faithful to that concept itself, then still > Cantor's diagonal argument applies to it. All of what I'm saying here > is that standard set theory as customarily understood doesn't not > restrict itself to a potential infinity context, but even if so then > if we faithfully represent that concept of potentiality then Cantor's > argument can be still carried on.