Comments by "Jeff Huffman" (@tejing2001) on "Is 1 a Prime Number?" video.

  1. It's too bad we don't actually teach the fundamental theorem of arithmetic in a fully qualified way... the most accurate way to say it is that each number, up to an invertible factor (1 and -1 for integers) has a decomposition into a unique product of primes, and some invertible factor. Said that way, it extends straightforwardly to more complex sets, such as the gaussian integers.
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  2.  @japanada11  Yeah, I forgot to add that unique factorization only applies to multiplicatively cancellable numbers, which discounts zero. Thanks for pointing that out. I would take the view that -3 is a prime number, but it's "the same" prime as 3. Viewed that way, 6 = 2*3, 6 = (-2)*(-3), -6 = (-2)*3, and -6 = 2*(-3) are all "the same" factorization of "the same" number. (This is slightly different from what I said before, I know.) Explained by example like that, I don't think it's too hard to follow, though the precise abstract statement is indeed too complex to use as an introduction to the subject. I just think it's a shame that when we teach it, we don't even address the issue of negative numbers at all.
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