+124 When doing an induction proof, why is it necessary in the hypothesis to assume it is true for the variable n to equal the variable k if they are both the same thing? In other words changing the letter you use doesn't change the math so what is the point of doing it? One could simply say that if you have proved the base case, where n is some number, n+1 is also in the sequence and so on and so forth, and using k wasn't necessary.
+118677 n is the variable in the question.
An example of a mathematical induction question is
For n > 1, 2 + 22 + 23 + 24 + ... + 2n = 2n+1 – 2
k is a specific integer. That means k is a constant.
So you
1) Show it is true for n=1
2) Then you assume it is true for a specific integer and you let that integer be k n=k
Using this assumption you prove it will be true fo the next integer where n=k+1
3) Then you know that one integer that k could have been was 1 (that means it is true for n=1) and you have proven that if it is true for one ingeter it must be true for the next so it will be true for n=2, n=3 etc.
So although it is a bit confusing, n and k are not exactly the same thing. n is a varable and k is a constant.
+1491 Because the induction proof is FORMAL and i don't know why but formal proofs make you do that sorta crud. I'm actually doing those as we speak. Wish me luck :c
