So I have to write a proof that "for every integer $x$, if $x$ is odd, then $x + 1$ is even". I understand what I have to do but I always get stuck at the last step which is prove that it's true for $k + 1$. Here's what I wrote down as my reasons as part of the proof:
- The theorem above is true for the base case (when $n=1$).
- Now lets assume the theorem is true for $n = k$.
- Now it's time to prove that the theorem is true for $n = k + 1$.
- If k is odd, then $(k + 1) + 1$ is even.
Is my rational/jump from $3$ to $4$ correct? I feel like I'm missing a step where I have to factor and algebraically solve the problem but I don't know how to go about that. Can someone please help me? Thanks!