# Induction proof

## Homework Statement

Prove that P(n,m) m+n = n+m for all m,n in natural numbers.

## The Attempt at a Solution

I prove by induction.

Base case: P(0,0) = 0+0 = 0+0.
Inductive step: Let n be an arbitrary natural number. Suppose m+n =n+m. Adding 2 to both sides of the equation gives us m+n+2 = n+m+2.(end of proof)

My question is if this is sufficient enough as a proof. (The instructor hinted us to show P(0,0) first. Then show P(n,0) and then proceed to P(n,m). The hint confuses me.

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## Homework Statement

Prove that P(n,m) m+n = n+m for all m,n in natural numbers.

## The Attempt at a Solution

I prove by induction.

Base case: P(0,0) = 0+0 = 0+0.
Inductive step: Let n be an arbitrary natural number. Suppose m+n =n+m. Adding 2 to both sides of the equation gives us m+n+2 = n+m+2.(end of proof)

My question is if this is sufficient enough as a proof. (The instructor hinted us to show P(0,0) first. Then show P(n,0) and then proceed to P(n,m). The hint confuses me.