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.

  • $\begingroup$ Hint: $k\ge 1 \Rightarrow k+1\ge 2$. $\endgroup$
    – rogerl
    Oct 1, 2018 at 1:01

1 Answer 1


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


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