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Every number has special properties :) Edit: In fact, I'd be astounded to encounter a number that did not exhibit any special properties. Until, of course, on
by coherentpony 13y ago
Every number has special properties :)
Edit: In fact, I'd be astounded to encounter a number that did not exhibit any special properties. Until, of course, one makes "having no special properties" a special property. In that case, I would no longer be astounded.
- quarterto 13y agoWe proceed by induction. Clearly n=1 is special, as it divides every integer. Assume k is special. If k+1 is not special, then it is special, as it is the first non-special number to come after a special number. This is a contradiction; then k+1 is special. ■
- samatman 13y agoWe may also proceed by ordinary semantics: every number is special, as it specifies itself.
- coherentpony 13y agoThat was extremely enjoyable to read.
- devgutt 13y agoCan you categorize the next non-special number in the same way? Now k+1 is no longer non-special, but the reason why it is special still exists, so you can't use it a second time.
- coherentpony 13y agoI think it was meant to be in jest.
- witek 13y agoI can't find it on the net, but in Umberto Eco's 'Foucault's Pendulum' the final monologue by the wife illustrates that really well.