Just had another quick thought - this is also the reason 1 isn't a prime; you can tag on 1 \times 1 \times 1 ... and still have the identical integer, so you lose unique prime factorisation. In larger fields, you specify unique prime factorisation *up to units* (where a unit has a multiplicative inverse, basically).
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Date: 2005-04-07 05:46 am (UTC)