# A strange inductive proof: Induction on $n$, for all positive integers $n,n\ge1$

Prove by induction on $$n$$ that, for all positive integers $$n, n\ge1$$.

My Try:

Base case is true for $$n=1$$.

Inductive step:

$$P(k)$$ is true. $$\implies k\ge1$$

We need to show that $$(k+1)\ge1$$

From here how should I proceed.

Can anyone explain this strange inductive proof.

• Hint: $k\ge 1 \Rightarrow k+1\ge 2$. – rogerl Oct 1 '18 at 1:01

$$k\ge1\implies k+1\ge1+1=2\gt1$$.