Are natural numbers isomorphic to complex numbers?
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From: Gerry Myerson on 1 Jun 2010 22:56 In article <4b309679-e046-43e4-b849-b54456dac38d(a)z17g2000vbd.googlegroups.com>, Arturo Magidin <magidin(a)member.ams.org> wrote: > On Jun 1, 7:16�pm, Akira Bergman <akiraberg...(a)gmail.com> wrote: > > On Jun 2, 5:05�am, "porky pig...(a)my-deja.com" <porky pig...(a)my- > > > > deja.com> wrote: > > > On Jun 1, 3:05�am, 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. > > > > > Thanks. May be you don't understand that, but with this reply you > > > instantly established your credentials. > > > > Don't jump on that one so eagerly. I was only confirming the meaning > > of the original question. There is no claim here. Only a question > > supported by an observation on the primes. > > Any "isomorphism", as the word is usually understood, requires among > other things a one-to-one identification between the two objects. > Since there can be no one-to-one identification between the natural > numbers and the complex numbers, the question has a trivial negative > answer, *regardless* of any observations made on primes or any other > objects, *unless* you wish to change the meaning of "isomorphic". or the meaning of N, or the meaning of C, or the meaning of "is". I wouldn't put any of those past OP. -- Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email)
From: Arturo Magidin on 1 Jun 2010 23:00 On Jun 1, 9:50 pm, Akira Bergman <akiraberg...(a)gmail.com> wrote: > On Jun 2, 12:30 pm, Arturo Magidin <magi...(a)member.ams.org> wrote: > > > And since this is trivial point for anyone who uses the word > > "isomorphism" knowing what it means, and knows some of the basic facts > > about real numbers (e.g., that they are *uncountable*), the comment > > about "credentials" was a pointed remark indicating that you were > > either talking about things you did not understand (e.g., the meaning > > "isomorphism"), or you were a crank (thinking that complex numbers are > > countable), or both. > > > Perhaps you can put that "knowledge" and intuition of yours behind > > some actual learning? > > > -- > > Arturo Magidin > > Now you are jumping. Porky's "credentials" comment was motivated (at > least in part) by my reply to his previous frivolous "my head > spinning" comment. He could not come back to that reply, so he jumped > on another more suitable one. His "thanks" was for giving him a chance > for a come back. > > I have not accepted your suggestion. Which suggests that you don't know what you are talking about. >I merely said I was going to > think about it. I am not here for empty debates. I just asked a > question. If you have a useful thing to say then say it, I did: you either have no clue, or your "question" has a *trivial*, *obvious*, *necessary* negative answer. > otherwise stop the politics. It's not politics; it was meant to be irony, since you proclaimed your own ego in your reply to Porky, talking about "knowledge", something that your entire participation in this thread shows you are entirely lacking in (at least with regards to the meaning of "isomorphism", "natural numbers", and "complex numbers"). -- Arturo Magidin
From: Jesse F. Hughes on 1 Jun 2010 23:29 Akira Bergman <akirabergman(a)gmail.com> writes: > On Jun 2, 12:30 pm, Arturo Magidin <magi...(a)member.ams.org> wrote: > >> And since this is trivial point for anyone who uses the word >> "isomorphism" knowing what it means, and knows some of the basic facts >> about real numbers (e.g., that they are *uncountable*), the comment >> about "credentials" was a pointed remark indicating that you were >> either talking about things you did not understand (e.g., the meaning >> "isomorphism"), or you were a crank (thinking that complex numbers are >> countable), or both. >> >> Perhaps you can put that "knowledge" and intuition of yours behind >> some actual learning? >> >> -- >> Arturo Magidin > > Now you are jumping. Porky's "credentials" comment was motivated (at > least in part) by my reply to his previous frivolous "my head > spinning" comment. He could not come back to that reply, so he jumped > on another more suitable one. His "thanks" was for giving him a chance > for a come back. Yes, that must be it. After all, a brilliant riposte like "Which part is spinning? The pork or the pig?" is simply devastating. Porky must have really been seething over the way you bested him like that. -- Jesse F. Hughes "But a 1 in base 3 represents a larger value than a 1 in base 7." -- Albert Wagner
From: Ostap Bender on 2 Jun 2010 01:27 On May 31, 4:14 pm, Akira Bergman <akiraberg...(a)gmail.com> wrote: > On May 31, 11:10 pm, 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? > > > -- > > I can't go on, I'll go on. > > N is a simple feedback summation structure with the initial value set > to 0; > > N(n+1) = N(n) + 1 > N(0) = 0 > > C has all the structures of N, Z and R, and on top of that, R is > rotated by pi/2 to make the polarized complex plane. It is a union of > the square with the circle. The decision involved in the solution of > the equation; > > x^2 = -1 > x = {+i,-i} > > enforces a spin onto the C. Could you please remind us what mapping you are using as your isomorphism between N and C?
From: Ostap Bender on 2 Jun 2010 01:30
On Jun 1, 7:20 pm, Akira Bergman <akiraberg...(a)gmail.com> wrote: > On Jun 2, 12:10 pm, Arturo Magidin <magi...(a)member.ams.org> wrote: > > > Any "isomorphism", as the word is usually understood, requires among > > other things a one-to-one identification between the two objects. > > Since there can be no one-to-one identification between the natural > > numbers and the complex numbers, the question has a trivial negative > > answer, *regardless* of any observations made on primes or any other > > objects, *unless* you wish to change the meaning of "isomorphic". > > > -- > > Arturo Magidin > > Good point. Thank you. More to think about. You haven't heard that the cardinality of C is "uncountable"? Never seen the "diagonalization" argument? |