Are natural numbers isomorphic to complex numbers?
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From: Akira Bergman on 31 May 2010 05:21 Euler's identity contains all the goodies; e^(i*Pi) = -1 'e' is implied in the natural numbers (N) by the density of the primes (P). How are 'i' and Pi included in N (if they are)? P/log(P) has a uniform density with fluctuations. Can these fluctuations be used to explain 'i' and Pi? I did some formant analysis on P/log(P) with Praat, and found 4 distinct patterns, probably corresponding to the four cycle nature of 'i'; i^n = 1,i,-1,-i,... ; n in N But I am not confident with his one. I have no idea how to explain Pi in N. Maybe through the Zeta function?
From: Gerry on 31 May 2010 07:26 On May 31, 7:21 pm, Akira Bergman <akiraberg...(a)gmail.com> wrote: > Euler's identity contains all the goodies; > > e^(i*Pi) = -1 > > 'e' is implied in the natural numbers (N) by the density of the primes > (P). Huh? > How are 'i' and Pi included in N (if they are)? They aren't. > P/log(P) has a uniform density with fluctuations. Huh?? > Can these fluctuations be used to explain 'i' and Pi? What is there to explain? > I did some formant analysis on P/log(P) with Praat, and found 4 > distinct patterns, probably corresponding to the four cycle nature of > 'i'; > > i^n = 1,i,-1,-i,... ; n in N > > But I am not confident with his one. I have no idea how to explain Pi > in N. Maybe through the Zeta function? Sure. Makes as much sense as anything else you've written here. -- GM
From: Don Stockbauer on 31 May 2010 08:07 Are natural numbers isomorphic to complex numbers? They are to me, but then, I never was too good at math.
From: Frederick Williams on 31 May 2010 09:10 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.
From: Stephen Montgomery-Smith on 31 May 2010 13:25
Akira Bergman wrote: > Euler's identity contains all the goodies; > > e^(i*Pi) = -1 > > 'e' is implied in the natural numbers (N) by the density of the primes > (P). > > How are 'i' and Pi included in N (if they are)? How about Euler's other identity sum 1/n^2 = pi^2 / 6. |