To solidfy how a proof by induction works, lets quickly go through a very simple example together. Prove that n =0 n >=0) Which of

To solidfy how a proof by induction works, lets quickly go through a very simple example together.

Prove that nn<n+1: (For now just focus on n>=0n>=0)

Which of the following could be appropriate base cases to use:

1 point

Let n=0n=0. Then it follows that 0<10<1 for nn<n+1

Let n=xn=x, where xx is some positive integer. Then xx<x+1.

2.

Question 2

Now that we have a base case, which of the following assumptions should we make?

1 point

Assume that nn<n+1

Assume that for all values up to n = kn=k, that n < n+1n<n+1.

3.

Question 3

Which of the following inductive steps finalizes our proof:

1 point

We can show that n=k+1n=k+1 allows for nn<n+1 to remain true for any k \geq 0k0.

(k+1)<(k+1)+1 ightarrow k+1k+1)<(k+1)+1k+1<k+21<2

Thus by induction we see our statement is true for any k \geq 0k0

We can show that n=k+1n=k+1 allows for nn<n+1 to remain true for any k \geq 1k1.

(k+1)<(k+1)+1 ightarrow k+1k+1)<(k+1)+1k+1<k+21<2