3 ms·

See https://news.ycombinator.com/item?id=29445794 https://news.ycombinator.com/item?id=29445794.

• auggierose 5y ago
  You explain how the induction step works. That step from n to n + 1 only works for n > 1. But 2 is not a proper base case. 3 is neither. Actually, the only potential base cases are 0 or 1. So the proper explanation why this argument doesn’t work is that the potential base cases are not covered by the induction step. And not that “the real base case is 2”.
  • poetically 5y ago
    Actually, now that I have explained the argument I realize it has nothing to do with induction. The logic of the argument is unrelated to induction, it's simply about functions that take constant values on some sets and what is required to extend a function to a larger set and conclude that it is constant on the larger set.
    • auggierose 5y ago
      Your argument still explains the induction step. In the end, P[n] => P[n+1] is just a statement that has “nothing to do with induction” once it is formed. You have obviously the right intuition about induction, but I think you are confused about its exact nature.
      • poetically 5y ago
        We'll have to agree to disagree then.