Are natural numbers isomorphic to complex numbers?
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From: Akira Bergman on 5 Jun 2010 00:57 On Jun 5, 2:39 pm, Ostap Bender <ostap_bender_1...(a)hotmail.com> wrote: > On Jun 4, 8:37 pm, Akira Bergman <akiraberg...(a)gmail.com> wrote: > > > "What is there to think about?!" > > > I know the meaning of isomorphism. It is pretty self explanatory. I > > did not want to give in because I am still intrigued by the > > possibility of the Euler's identity being imprinted on N somehow, like > > e is through the density of primes. > > But what does that have to do with isomorphisms? "Isomorphic" means > "has exactly the same structure". Even if we forgot the topological > and cardinality differences between N and C, how can you think that > they can have the same algebraic structure, given that C is is an > algebraically closed field, and N is not even closed under > subtraction? It means that N has all of the information that C has. You just have to know how to look at it. > > > I had been rewarded for following my hunch few times and did not want > > to abandon it because of formalism. Look at the 0^0 discussion I > > initiated many years ago as a good example. > > No, thank you. I am not interested in hot air games. The hot air games are inside your head. Just like your claim about me abusing JJ for no reason. Show me one original finding that belongs to you if you can come out of your hiding behind that alias. It is easy to abuse people from behind an alias. > > > Until I proved that case, > > there was strong opposition. > > > I now see that my criticisms of the academia was unfair and too > > general. I realized thit more after discussing with Magidin and > > experiencing his patience and strength. > > Yes, his patience is as always remarkable. He tolerated an enormous > amount of unjust abuse from you.
From: Ostap Bender on 5 Jun 2010 01:19 On Jun 4, 9:57 pm, Akira Bergman <akiraberg...(a)gmail.com> wrote: > On Jun 5, 2:39 pm, Ostap Bender <ostap_bender_1...(a)hotmail.com> wrote: > > > On Jun 4, 8:37 pm, Akira Bergman <akiraberg...(a)gmail.com> wrote: > > > > "What is there to think about?!" > > > > I know the meaning of isomorphism. It is pretty self explanatory. I > > > did not want to give in because I am still intrigued by the > > > possibility of the Euler's identity being imprinted on N somehow, like > > > e is through the density of primes. > > > But what does that have to do with isomorphisms? "Isomorphic" means > > "has exactly the same structure". Even if we forgot the topological > > and cardinality differences between N and C, how can you think that > > they can have the same algebraic structure, given that C is is an > > algebraically closed field, and N is not even closed under > > subtraction? > > It means that N has all of the information that C has. You just have > to know how to look at it. Of course N has all of the information that C has. C is derived from N in a very canonical way. But that has nothing to do with isomorphism. FYI: http://en.wikipedia.org/wiki/Isomorphism An isomorphism (Greek: á¼´ÏÎ¿Ï isos "equal", and μοÏÏή morphe "shape") is a bijective map f such that both f and its inverse f â1 are homomorphisms, i.e., structure-preserving mappings. It may be the case that a single atom contains all the information about the entire Universe, but it is hard to see than an atom and the Universe are isomorphic. > > > I had been rewarded for following my hunch few times and did not want > > > to abandon it because of formalism. Look at the 0^0 discussion I > > > initiated many years ago as a good example. > > > No, thank you. I am not interested in hot air games. > > The hot air games are inside your head. How did you figure THAT? I assure you that to me, there exist much more satisfying and challenging mental activities than the philosophical discussions on the meaning of 0^0. > Just like your claim about me > abusing JJ for no reason. I made no such claim. You continue to misunderstand the reason why I brought up the JJ case. > Show me one original finding that belongs to > you if you can come out of your hiding behind that alias. You want me to provide you with the list of my journal publications? No, I don't want to disclose my real name. If my real name became public, I would be at the mercy of too many kooks. I saw a friend of mine lose his job because he signed his posts with his real name. > It is easy > to abuse people from behind an alias. Not true. I have made thousands of posts to Usenet under my current alias, so you are welcome to attack all these posts if you find them laughable or hypocritical. I am not attacking you for your real-life activity either. Only for your Usenet posts. Moreover, being aware of the famous film directors Akira Kurosawa and Ingmar Bergman, I suspect your own nick "Akira Bergman" is an alias. Care to give us your REAL name? Or do you prefer to abuse people from behind an alias?
From: Akira Bergman on 5 Jun 2010 01:39 On Jun 5, 3:19 pm, Ostap Bender <ostap_bender_1...(a)hotmail.com> wrote: > On Jun 4, 9:57 pm, Akira Bergman <akiraberg...(a)gmail.com> wrote: > > > > > > > On Jun 5, 2:39 pm, Ostap Bender <ostap_bender_1...(a)hotmail.com> wrote: > > > > On Jun 4, 8:37 pm, Akira Bergman <akiraberg...(a)gmail.com> wrote: > > > > > "What is there to think about?!" > > > > > I know the meaning of isomorphism. It is pretty self explanatory. I > > > > did not want to give in because I am still intrigued by the > > > > possibility of the Euler's identity being imprinted on N somehow, like > > > > e is through the density of primes. > > > > But what does that have to do with isomorphisms? "Isomorphic" means > > > "has exactly the same structure". Even if we forgot the topological > > > and cardinality differences between N and C, how can you think that > > > they can have the same algebraic structure, given that C is is an > > > algebraically closed field, and N is not even closed under > > > subtraction? > > > It means that N has all of the information that C has. You just have > > to know how to look at it. > > Of course N has all of the information that C has. C is derived from N > in a very canonical way. > > But that has nothing to do with isomorphism. FYI: > > http://en.wikipedia.org/wiki/Isomorphism > An isomorphism (Greek: á¼´ÏÎ¿Ï isos "equal", and μοÏÏή morphe "shape") is > a bijective  map f such that both f and its inverse f â1 are > homomorphisms, i.e., structure-preserving mappings. > > It may be the case that a single atom contains all the information > about the entire Universe, but it is hard to see than an atom and the > Universe are isomorphic. > > > > > I had been rewarded for following my hunch few times and did not want > > > > to abandon it because of formalism. Look at the 0^0 discussion I > > > > initiated many years ago as a good example. > > > > No, thank you. I am not interested in hot air games. > > > The hot air games are inside your head. > > How did you figure THAT? I assure you that to me, there exist much > more satisfying and challenging mental activities than the > philosophical discussions on the meaning of 0^0. Not only philosophical, but also mathematical; 0^0 = {0,1} x^y = e^(y*log(x)) > > > Just like your claim about me > > abusing JJ for no reason. > > I made no such claim. You continue to misunderstand the reason why I > brought up the JJ case. > > > Show me one original finding that belongs to > > you if you can come out of your hiding behind that alias. > > You want me to provide you with the list of my journal publications? > No, I don't want to disclose my real name. If my real name became > public, I would be at the mercy of too many kooks. I saw a friend of > mine lose his job because he signed his posts with his real name. > > > It is easy > > to abuse people from behind an alias. > > Not true. I have made thousands of posts to Usenet under my current > alias, so you are welcome to attack all these posts if you find them > laughable or hypocritical. > > I am not attacking you for your real-life activity either. Only for > your Usenet posts. > > Moreover, being aware of the famous film directors Akira Kurosawa and > Ingmar Bergman, I suspect your own nick "Akira Bergman" is an alias. > Care to give us your REAL name?  Or do you prefer to abuse people from > behind an alias? Akira Bergman is the name on my passport. I am not scared of anybody for my activities anywhere. I have no need to hide.
From: Ostap Bender on 5 Jun 2010 01:55 On Jun 4, 10:39 pm, Akira Bergman <akiraberg...(a)gmail.com> wrote: > On Jun 5, 3:19 pm, Ostap Bender <ostap_bender_1...(a)hotmail.com> wrote: > > > > > On Jun 4, 9:57 pm, Akira Bergman <akiraberg...(a)gmail.com> wrote: > > > > On Jun 5, 2:39 pm, Ostap Bender <ostap_bender_1...(a)hotmail.com> wrote: > > > > > On Jun 4, 8:37 pm, Akira Bergman <akiraberg...(a)gmail.com> wrote: > > > > > > "What is there to think about?!" > > > > > > I know the meaning of isomorphism. It is pretty self explanatory. I > > > > > did not want to give in because I am still intrigued by the > > > > > possibility of the Euler's identity being imprinted on N somehow, like > > > > > e is through the density of primes. > > > > > But what does that have to do with isomorphisms? "Isomorphic" means > > > > "has exactly the same structure". Even if we forgot the topological > > > > and cardinality differences between N and C, how can you think that > > > > they can have the same algebraic structure, given that C is is an > > > > algebraically closed field, and N is not even closed under > > > > subtraction? > > > > It means that N has all of the information that C has. You just have > > > to know how to look at it. > > > Of course N has all of the information that C has. C is derived from N > > in a very canonical way. > > > But that has nothing to do with isomorphism. FYI: > > >http://en.wikipedia.org/wiki/Isomorphism > > An isomorphism (Greek: á¼´ÏÎ¿Ï isos "equal", and μοÏÏή morphe "shape") is > > a bijective  map f such that both f and its inverse f â1 are > > homomorphisms, i.e., structure-preserving mappings. > > > It may be the case that a single atom contains all the information > > about the entire Universe, but it is hard to see than an atom and the > > Universe are isomorphic. > > > > > > I had been rewarded for following my hunch few times and did not want > > > > > to abandon it because of formalism. Look at the 0^0 discussion I > > > > > initiated many years ago as a good example. > > > > > No, thank you. I am not interested in hot air games. > > > > The hot air games are inside your head. > > > How did you figure THAT? I assure you that to me, there exist much > > more satisfying and challenging mental activities than the > > philosophical discussions on the meaning of 0^0. > > Not only philosophical, but also mathematical; > > 0^0 = {0,1} > x^y = e^(y*log(x)) Wasn't it decided by almost complete consensus back in the 19th century that Euler was right and that it is best to set 0^0 = 1 ? Is that what you advocate too? > > > Just like your claim about me > > > abusing JJ for no reason. > > > I made no such claim. You continue to misunderstand the reason why I > > brought up the JJ case. > > > > Show me one original finding that belongs to > > > you if you can come out of your hiding behind that alias. > > > You want me to provide you with the list of my journal publications? > > No, I don't want to disclose my real name. If my real name became > > public, I would be at the mercy of too many kooks. I saw a friend of > > mine lose his job because he signed his posts with his real name. > > > > It is easy > > > to abuse people from behind an alias. > > > Not true. I have made thousands of posts to Usenet under my current > > alias, so you are welcome to attack all these posts if you find them > > laughable or hypocritical. > > > I am not attacking you for your real-life activity either. Only for > > your Usenet posts. > > > Moreover, being aware of the famous film directors Akira Kurosawa and > > Ingmar Bergman, I suspect your own nick "Akira Bergman" is an alias. > > Care to give us your REAL name?  Or do you prefer to abuse people from > > behind an alias? > > Akira Bergman is the name on my passport. I am not scared of anybody > for my activities anywhere. I have no need to hide. Are you self-employed?
From: Akira Bergman on 5 Jun 2010 02:19
"Wasn't it decided by almost complete consensus back in the 19th century that Euler was right and that it is best to set 0^0 = 1 ? Is that what you advocate too? " It is self explanatory from x^y = e^(y*log(x)). It has been on the net for years and still gets good traffic. It was agreed by sci.math crowd years ago. I don't know how it has been missed by so many math-heads for so many years. This is what I mean by the pitfalls of formalism heavy thinking. I don't have to advocate it. It advocates itself. "Are you self-employed?" I don't have to work for a while. There is nothing like freedom from doing others work. |