Find the error in the proof.
This is the question:
Theorem: Every positive integer is equal to the next largest positive integer.
Proof: Let $P(n)$ be the proposition that $n=n+1$.To show that $P(k)$ implies $P(k+1)$, assume $P(k)$ is true such that $k=k+1$. Adding 1 on both sides we get $k+1=k+2$. Which is nothing but $P(k+1)$. Thus, $P(k)-P(k+1)$ is true. Hence $P(n)$ is true for all positive integers $n$.
On
The how of a Proof by Induction works is often explained by analogy to "showing that a chain of dominos will fall."
You have successfully shown that if any tile is tipped, then the subsequent tile in the chain will also tip. $$\forall n\geq 1: p(n)\to p(n+1)$$
However, you have neglected to show that the first tile in the chain can be tipped, rather than being set up firmly against a wall; as in fact is the case. $$\require{cancel} \xcancel{p(1)}$$
Is it $P(1)$ true? Is it $1=2?$
When you apply induction you need two things:
In your case the first condition fails.