The first time I saw the proof I was not satisfied because I wondered why you couldn't use the same exact argument to show the integers are uncountable (and back in high school I didn't grasp the quick answer, 'because only reals have infinite digits, any particular integer only has finite digits').<p>I remember Mark Krusemeyer at MC took a more satisfying approach.  He first showed the power set of integers was uncountable, then showed the one-to-one / onto mapping to the reals (and then some bit about power sets of power sets as a way of finding ever larger and more infinite sets).<p>For whatever reason, thinking of the size of power sets seem a bit less abstract than the size of reals, maybe because it feels more discrete and computer science-ish?