Theorem: Fundamental Theorem of Arithmetic

19 March 2012, 19:29


This photo is taken from just outside Ivan’s room.

I’ll get to a real interesting theorem sometime. Hopefully. This one is pretty nifty. It’s even one of those Fundamental theorems. Like the one that basically says calculus works, bitches! Which I won’t get in to, because it’s dull.

Theorem: Let $n$ be a member of $\mathbb{Z}^+ \setminus \{1\}$. Then $n$ can be written as a unique product of prime numbers.

I’m not going to prove this. Because I can’t be bothered. It’s not that hard, being in Euclid and all that. Basically. Anyway, the important word to note is unique. There is some fiddling, as you can write $6 = 2 \cdot 3$ and $6 = 3 \cdot 2$ (yay for isomorphisms). Oh, another consequence of this is that 1 is not prime. Not that it ever was in the first place. Though some people seem to think that it is. If you find one, hit them with a large stick. Or be polite and say “Sir, I do believe you are mistaken”.

Posted by Michael Welsh at 06:29.

Comment

  1. Your use of the word “consequence” is interesting. Basically, I agree: 1 is not a prime as a consequence of the theorem, but of course this is not a logical consequence at all but an aesthetic one, viz. if 1 were a prime, the theorem would be ugly.

    I once book-blocked your sister w.r.t. the Hitchhiker’s Guide collection; if she still wants it she can have it, as I am throwing it away.

    — J'Bosh · 8 April 2012, 14:38 · #

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