Indeed, the integers have the same limitation -- factorization is unique only up to units. 1 = -1 * -1 In elementary mathematics, people wave away "-1" by say

Indeed, the integers have the same limitation -- factorization is unique only up to units. 1 = -1 * -1 In elementary mathematics, people wave away "-1" by saying silly things like "positive integers", before Gaussian integers arrive and force us to figure out precisely what we are trying to say without silly ideas from analysis like "ordering". :-)