5 ms·
Where exactly is my error?
by poetically 5y ago
Where exactly is my error?
- auggierose 5y agoIn your first sentence. What is the inductive invariant you are talking about?
- poetically 5y agoSee https://news.ycombinator.com/item?id=29445794 https://news.ycombinator.com/item?id=29445794.
- auggierose 5y agoYou 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 agoActually, 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 agoYour 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 agoWe'll have to agree to disagree then.
- Rexxar 5y agoYou prove "n+1=>n" instead of "n=>n+1"
- poetically 5y agoI don't think so but we can agree to disagree.
- Rexxar 5y agoIn your induction you start by "Consider a set of n+1 horse" then conclude "By the inductive hypothesis, all of the n remaining horses are the same color". You did the induction in the wrong direction. "We can agree to disagree" is not a valid mathematical in my opinion. At least one of us is wrong (and maybe we are both wrong).
- auggierose 5y agoWell, in this case, you are wrong ;-)