I am given a strict inequality of the form $$ 2n - 8 < n^2-8n+14, $$ where $n$ belongs to the set of natural numbers $\mathbb{N}$ (in this case $n$ does not equal 0).
I am asked, for what values of $n$ is the above inequality true?
Upon tabulating the various inputs and outputs, I find that it appears that the inequality is true for $\mathbb{N} \setminus \{4,5,6\}$.
Am I supposed to then proceed with induction with the new set of natural numbers, and if so, how many base cases do I need to establish, that is, do I go up to $n=3$ and then to $n = 7$, for instance?
I hope that makes sense.