Timeline for Definability of arithmetic functions and relations
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 20, 2014 at 6:23 | comment | added | Andreas Blass | @HansStricker The existence of those automorphisms is essentially the fundamental theorem of arithmetic, that every natural number admits a unique factorization into primes. So, for multiplicative purposes, all the information about a natural number $n$ is in the exponents $e_2,e_3,e_5,\dots$ of the primes $2,3,5,\dots$ in the factorization of $n$. Multiplying numbers amounts to adding corresponding exponents. From this viewpoint, it's obvious that permuting the primes amounts to just listing the exponents in a different order and doesn't affect the structure. | |
| Aug 20, 2014 at 6:07 | comment | added | Hans-Peter Stricker | Are those automorphisms something "everybody" should know - or is it somehow advanced knowledge? Googling for "permutation(s) of (the) primes" yields very little results. Do you have a reference, eventually? Thanks in advance. | |
| Aug 19, 2014 at 15:25 | comment | added | Hans-Peter Stricker | Thank you! I didn't think about the problem in terms of automorphisms. But obviously that's the right perspective. | |
| Aug 19, 2014 at 15:24 | vote | accept | Hans-Peter Stricker | ||
| Aug 19, 2014 at 15:23 | history | answered | Andreas Blass | CC BY-SA 3.0 |