4 ms·
We 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
by quarterto 13y ago
We 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.