00:01
All right, so this is a long question, so i'm not going to rewrite the whole question.
00:06
I'm just going to make a quick recap on the principle of mathematical induction.
00:12
So, of course, the problem is not here about the base case, right? we can start the base case from 0, 1, 2, 5, 10, it doesn't matter, and then we prove it for all numbers above that base case.
00:23
But essentially, what we have to do, let's say, we take our base case and we prove the proposition for our base case is true.
00:30
All right, n0, some integer, write some natural number, some natural number or zero, right? we prove this one is true, and then we prove that.
00:45
Pk implies pk plus 1 for all k greater than or equal to n0.
00:53
Right.
00:54
And then these implies these two together imply then that pn true for all n, great and equal to n0.
01:04
Essentially, it is you proof for the first piece of the domino, and then you prove that if all pieces, if one piece falls, then the next one also falls.
01:14
But in particular, you need the first piece to fall...