Are natural numbers isomorphic to complex numbers?
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From: Transfer Principle on 1 Jun 2010 01:42 On May 31, 6:10 am, Frederick Williams <frederick.willia...(a)tesco.net> wrote: > Don Stockbauer wrote: > > Are natural numbers isomorphic to complex numbers? > > They are to me, but then, I never was too good at math. > An isomorphism is (among other things) a map that preserves structure. > What structure do N and C have? > An isomorphism is (among other things) a map that is onto. What map > from N to C is onto? Do Bergman and Stockbauer mean that N is isomorphic to C, or that N is isomorphic to a _subset_ of C? (Leaving out the words "a subset of" led to a huge argument in another recent thread.)
From: Akira Bergman on 1 Jun 2010 03:05 On Jun 1, 3:42 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > Do Bergman and Stockbauer mean that N is isomorphic to C, > or that N is isomorphic to a _subset_ of C? (Leaving out > the words "a subset of" led to a huge argument in another > recent thread.) I mean N is isomorphic to C.
From: Akira Bergman on 1 Jun 2010 03:29 On Jun 1, 3:40 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > Now how Bergman proceeds is mysterious to me. It appears > that he looks at the function g(n) = n/ln(n) and somehow > notices 4-periodic behavior in that function. But it > escapes me what pattern Bergman found that would be > related to 4-periodicity. Thanks TP for your clearer and more formal explanations and the additional information and questions. While I am looking further into the other points you raised, I like to respond to this paragraph now. I have run into difficulties confirming this claim (I already noted before that I was not confident with this one). I need to learn how Praat formant analysis works. This may take time.
From: David C. Ullrich on 1 Jun 2010 05:37 On Tue, 1 Jun 2010 00:05:56 -0700 (PDT), Akira Bergman <akirabergman(a)gmail.com> wrote: >On Jun 1, 3:42�pm, Transfer Principle <lwal...(a)lausd.net> wrote: > >> Do Bergman and Stockbauer mean that N is isomorphic to C, >> or that N is isomorphic to a _subset_ of C? (Leaving out >> the words "a subset of" led to a huge argument in another >> recent thread.) > >I mean N is isomorphic to C. Good of you to clarify that. That's ridiculous, by the way. Obviously ridiculous, for many obvious reasons.
From: Don Stockbauer on 1 Jun 2010 08:17
On Jun 1, 4:37 am, David C. Ullrich <ullr...(a)math.okstate.edu> wrote: > On Tue, 1 Jun 2010 00:05:56 -0700 (PDT), Akira Bergman > > <akiraberg...(a)gmail.com> wrote: > >On Jun 1, 3:42 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > >> Do Bergman and Stockbauer mean that N is isomorphic to C, > >> or that N is isomorphic to a _subset_ of C? (Leaving out > >> the words "a subset of" led to a huge argument in another > >> recent thread.) > > >I mean N is isomorphic to C. > > Good of you to clarify that. > > That's ridiculous, by the way. Obviously ridiculous, for many > obvious reasons. 5 DEBATE GO TO 5 |