Uncountability of the Rationals?
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From: MoeBlee on 11 Jun 2010 13:59 On Jun 11, 8:46 am, Tony Orlow <t...(a)lightlink.com> wrote: > omega/2 What operation is '/' where <w 2> are in the domain? Ordinal division? It's not cardinal division, until you DEFINE such a thing. MoeBlee
From: MoeBlee on 11 Jun 2010 14:01 On Jun 11, 8:58 am, Tony Orlow <t...(a)lightlink.com> wrote: > If you don't understand it how can > you criticize it? As you don't understand ZFC. And as we don't understand Orlowism, because you've never given a coherent formulation of it. MoeBlee
From: MoeBlee on 11 Jun 2010 14:14 On Jun 11, 8:48 am, Tony Orlow <t...(a)lightlink.com> wrote: > My ideas are clearly at odds with > transfinite set theory. Last I heard from you about this, you said that you don't contest ZFC itself but only the way ZFC has been "extended" (or whatever your exact words; and whatever you might MEAN by that). When I attempted (wasting my good time) to sort that out with you, the conversation ended up nowhere. MoeBlee
From: MoeBlee on 11 Jun 2010 14:17 On Jun 11, 11:44 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > one can prove that omega is the least infinite ordinal (where > "least" is defined in terms of cardinality, of course). We don't even need cardinality. We prove that if S is an infinite ordinal then w is a subset of S and that there is no other infinite ordinal that is a subset of all infinite ordinals. MoeBlee
From: MoeBlee on 11 Jun 2010 14:27
> >> Tony Orlow wrote: > >> > 0<1 > >> > x<y -> E z: x<z<y > > >> > This leads to some level of infinites between counting numbers. Not if those are self-standing axioms. (Do you mean to add that < is irreflexive?) MoeBlee |