The Definition of Points
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From: MoeBlee on 2 Apr 2007 12:51 On Mar 31, 5:39 am, Tony Orlow <t...(a)lightlink.com> wrote: > In order to support the notion of aleph_0, one has to discard the basic > notion of subtraction in the infinite case. That seems like an undue > sacrifice to me, for the sake of nonsense. Sorry. For the sake of a formal axiomatization of the theorems of ordinary mathematics in analysis, algebra, topology, etc. But please do let us know when you have such a formal axiomatization but one that does have cardinal subtraction working in the infinite case just as it works in the finite case. MoeBlee
From: Virgil on 2 Apr 2007 15:51 In article <4611182b(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > It's true that the set of consecutive naturals starting at 1 with size x > has largest element x. Not unless x is less than or equal to some natural. > Is N of that form? It is if x >= aleph_0.
From: Lester Zick on 2 Apr 2007 17:36 On 2 Apr 2007 08:39:25 -0700, "Mike Kelly" <mikekellyuk(a)googlemail.com> wrote: >Is ranting incoherently just your way of blowing off steam? It seems to be yours. ~v~~
From: Lester Zick on 2 Apr 2007 17:37 On Mon, 2 Apr 2007 16:12:46 +0000 (UTC), stephen(a)nomail.com wrote: >> It is not true that the set of consecutive naturals starting at 1 with >> cardinality x has largest element x. A set of consecutive naturals >> starting at 1 need not have a largest element at all. > >To be fair to Tony, he said "size", not "cardinality". If Tony wishes to define >"size" such that set of consecutive naturals starting at 1 with size x has a >largest element x, he can, but an immediate consequence of that definition >is that N does not have a size. Is that true? ~v~~
From: Lester Zick on 2 Apr 2007 17:37
On 2 Apr 2007 09:24:06 -0700, "Mike Kelly" <mikekellyuk(a)googlemail.com> wrote: > Who he thinks he is fooling is beyond me. There is a lot beyond you. ~v~~ |