3 ms·

I have been fascinated by these integrals for a long time and am happy to see them getting more attention. 3Blue1Brown recently made a video on the topic: http

• _nalply 4y ago
  To prove something for all n you need to do mathematical induction: First prove that something is true for some n, usually n = 1. Then prove that if it's true for n it's for n + 1, too. Boom. It's true for all n. But the second step is sometimes very hard or even perhaps impossible.
  • Chinjut 4y ago
    Induction is one way to prove something for all n but hardly the only way.
  • galaxyLogic 4y ago
    > Then prove that if it's true for n it's for n + 1, too. Or you might be able to prove that it is true for n + 2 but not be able to prove it is true for n + 1. Right?
• c7b 4y ago
  > What strikes me is the reminder that it is never possible to "prove" something by pointing out that it is true for all known cases. Not exactly true. If you can prove that the cases you checked amount to all the cases in the theorem statement, you're done. The Four-color theorem is a well-known example that was originally proved in this way (accompanied by a controversy about whether that's a 'real' proof, which is arguably pretty much settled at this point). Induction would arguably be another way (that only requires checking a single case).