Would I need to show P(n+1,0) and P(0,m+1) or would P(n,0) and P(m) be sufficient? Because I know that for the inductive step we prove if P(n) then P(n+1).
Homework Statement
Prove that P(n,m) m+n = n+m for all m,n in natural numbers.
Homework Equations
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...