It doesn't say that. It says k+1>2 which it is because k is at least 4. In fact, k+1>4, but all that's needed for the proof is k+1>2.
Also you have a typo. That minus sign towards the end should be an equal sign.
This is given as an example of proof by induction. Prove that for all n >= 4
and . Thus is true. Now suppose that k >= 4 and the statement is true for n=k. Thus we suppose We must prove that the statement is true for n=k+1; that is, we must prove that . Now
using the induction hpothesis. Since k >= 4 certainly k+1 > 2 so . We conclude that as desired. By the principle of mathematical induction we conclude that for all integers n>=4
I don't get the part after "certainly k+1>2". What happened to the factorial?
It doesn't say that. It says k+1>2 which it is because k is at least 4. In fact, k+1>4, but all that's needed for the proof is k+1>2.
Also you have a typo. That minus sign towards the end should be an equal sign.