Galileo's Paradox
in [Math]
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From: Virgil on 11 Dec 2006 17:03 In article <457d95fb(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > > Does TO claim that the infinite numbers of Robinson's non-standard > > analysis are in any way connected to the transfinite cardinals and > > ordinals of Cantor's analyses? Pray tell what ultrafilter generates > > standard cardinals and ordinals in the way that ultrafilters are needed > > to construct Robinson's non-standard reals from standard reals. > > I claimed no such thing. I am saying his very reasonable approach > directly contradicts the very concept of the limit ordinals How does it do that? As there are n ordinals in his non-standard reals, and discussion of ordinality is irrelevant in his system.
From: Virgil on 11 Dec 2006 17:05 In article <457d965d(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <457cc0ce(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> I suppose now you're going to tell me I'm using nonstandard language.... > > > > Almost always, as far as the meaning of standard mathematical terms goes. > > Did you at least learn what a formal language is now? I remember you > taking issue with me about the "null string" as if no such thing > existed. Where pray tell did I ever do that?. Besides, in a sort of sense, isn't being a null string about as non-existent as a string can get?
From: Lester Zick on 11 Dec 2006 17:38 On Mon, 11 Dec 2006 12:32:57 -0500, Bob Kolker <nowhere(a)nowhere.com> wrote: >Eckard Blumschein wrote:> >> No. Cantor again merely showed by contradiction that the power set is >> not countable. The reason is: Already the entity of all natural numbers >> is an uncountable fiction. > >By definition, the set of integers is countable. Is that true? > A countable infinite >set is a set which can be put in one to one correspondence with the set >of integers. So a countable infinite set is a set which can be put in one to one correspondence with the countable set of integers? So "countable" means "infinite"? 3.14159 . . . ~v~~
From: MoeBlee on 11 Dec 2006 17:45 Virgil wrote: > In article <457d965d(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > > > Virgil wrote: > > > In article <457cc0ce(a)news2.lightlink.com>, > > > Tony Orlow <tony(a)lightlink.com> wrote: > > > > > >> I suppose now you're going to tell me I'm using nonstandard language.... > > > > > > Almost always, as far as the meaning of standard mathematical terms goes. > > > > Did you at least learn what a formal language is now? I remember you > > taking issue with me about the "null string" as if no such thing > > existed. > > > Where pray tell did I ever do that?. > > Besides, in a sort of sense, isn't being a null string about as > non-existent as a string can get? The null string is the empty set. It exists. MoeBlee
From: Virgil on 11 Dec 2006 18:10
In article <1165877125.676999.17400(a)73g2000cwn.googlegroups.com>, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > Virgil wrote: > > In article <457d965d(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > > > Virgil wrote: > > > > In article <457cc0ce(a)news2.lightlink.com>, > > > > Tony Orlow <tony(a)lightlink.com> wrote: > > > > > > > >> I suppose now you're going to tell me I'm using nonstandard > > > >> language.... > > > > > > > > Almost always, as far as the meaning of standard mathematical terms > > > > goes. > > > > > > Did you at least learn what a formal language is now? I remember you > > > taking issue with me about the "null string" as if no such thing > > > existed. > > > > > > Where pray tell did I ever do that?. > > > > Besides, in a sort of sense, isn't being a null string about as > > non-existent as a string can get? > > The null string is the empty set. It exists. But, as I said, is about as non-existent as a string can get. Any less existent and it wouldn't be a string at all. |