Re: Relative Cardinality



Virgil wrote:

>
> For any two infinite disjoint sets, their union can be so ordered, at
> least if one allows AC, that either appears to be the smaller. Thus WM
> is claiming that all infinite sets are of the same cardinality.
>
> Such a presumption need not be accepted.

Ask Ross!

Of course there is only one infinity, namely the potential one. Hence
you are correct. Otherwise explain: Why is my criterion that
misleading?

Regards, WM

.

Relevant Pages

  • Re: Orlow cardinality question
    ... N is the union of all its initial segments. ... > naturals to be infinite, ... for N limited to only finite naturals: ... > When will Virgil wake up to the fact that he doesn't know everything ...
    (sci.math)
  • Re: Relative Cardinality
    ... > Virgil wrote: ... >> For any two infinite disjoint sets, their union can be so ordered, at ... >> is claiming that all infinite sets are of the same cardinality. ...
    (sci.math)
  • Re: Relative Cardinality
    ... Virgil ... WM's "relative cardinality" at least as defined, ... but a property of infinite sets ... set of irrationals comprises more elements than the set of reals? ...
    (sci.math)
  • Re: Cantor Confusion
    ... The union of finite trees contains an infinite tree. ... The union of finite chains contains an infinite chain. ... If there is an infinite pathlength, then there must be an infinite ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... To be honest I'm impressed with Tony. ... > Virgil basically attacks Tony, and as above tries to segregate him. ... I think Virgil has a very vested interest in the standard model. ... "uuncountably" infinite set, without the kind of discontinuities we find in the ...
    (sci.math)