Let [itex](N, s(n), 0)[/itex] be a Peano space. That is, [itex]N=\{1,2,3,\dots \}[/itex] is a set in which http://en.wikipedia.org/wiki/Peano_arithmetic" [Broken] can be used.(adsbygoogle = window.adsbygoogle || []).push({});

We can then define:

- [itex]0=\varnothing, 1=\{0\}, 2=\{0,1\},\dots \implies n=\{0,1,2,\dots ,n-2,n-1\}[/itex]

- [itex]s(a)=a\cup \{a\}\implies s(a)=a+1[/itex]

From here we can define both addition and multiplication. I was wondering how the properties of primes come to be. That is, what makes [itex]19=\{0,1,2,\dots ,18\}[/itex] prime and [itex]4=\{0,1,2,3\}[/itex] not prime.

I've never really studied Number Theory, so I'm not strong in it at all.

(If you've noticed, I really like Peano spaces)

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# How do primes come out of Peano arithmetic?

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