(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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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# Induction proof

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