On 2/26/2014 4:11 PM, Martin Shobe wrote: > On 2/26/2014 4:27 PM, Dan Christensen wrote: >> On Wednesday, February 26, 2014 4:31:24 PM UTC-5, Virgil wrote: >>> In article <email@example.com>, >>> Dan Christensen <Dan_Christensen@sympatico.ca> wrote: >>>> If you want to claim that there are no infinite sets, you might have >>>> a point. >>>> For every Dedekind-infinite set S, however, there exists a subset of >>>> S which >>>> satisfy Peano's axioms -- a "copy" of the natural numbers, if you >>>> will. And >>>> that's no "juvenile rot". > >>> What about sets being infinite but not Dedekind-infinite? > >> Can you give an example? > > You were told on math.stackexchange that you can't be given an explicit > example. You were even told why. Why are you asking for an example here? > > Martin Shobe >
He's compelled by it, these "sub-numerous" and other notions in the infinite are simple features of constructive domains. DC simply trusts his own mathematical intuition.
Heh, I wrote a question on math.stackexchange.com and nobody would answer it. ("Simple analytical properties of n/d, d -> oo, n -> d", or as it is.) The answer I got was this: " ".
Then on Math Overflow basically as an answer to a question, with an alternative implementation, this was the counterargument with m >> n as on Math Overflow and my Blog.
I have a crushing intellect, inspiration inspires me.
So, kudos, quite, go on, Shobe have you ever heard "sub-numerous"?
I wrote a definition for infinite, at the time, claiming it distinct from our quite standard definitions of Dedekind and Tarski here, this of course interpretable with the Archimedean definitions, in parts and for the variety, in infinity.
And rather: this isn't a question and answer forum.