Are natural numbers isomorphic to complex numbers?
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From: Akira Bergman on 1 Jun 2010 20:16 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. Besides, credentials are not my main motivation. I suggest that you should put that ego of yours behind your knowledge and intuition.
From: Arturo Magidin on 1 Jun 2010 22:10 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". -- Arturo Magidin
From: Akira Bergman on 1 Jun 2010 22:20 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.
From: Arturo Magidin on 1 Jun 2010 22:30 On Jun 1, 9:20 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". > Good point. Thank you. More to think about. 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
From: Akira Bergman on 1 Jun 2010 22:50
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. 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, otherwise stop the politics. |