- #1
samkolb
- 37
- 0
If I am given a propisition P(m,n) and asked to show that it is true for all integers m and n, how do I go about that?
My strategy is to fix one of the variables, say m, and then proceed to use induction on n. Once I've shown that P(m,n) holds for all n when m is fixed, I then conclude that P(m,n) holds for all m and n, since m was chosen arbitrarily.
Is this correct?
If it helps, the particular problem I'm working on is proving the laws of exponents for a group.
Sam
My strategy is to fix one of the variables, say m, and then proceed to use induction on n. Once I've shown that P(m,n) holds for all n when m is fixed, I then conclude that P(m,n) holds for all m and n, since m was chosen arbitrarily.
Is this correct?
If it helps, the particular problem I'm working on is proving the laws of exponents for a group.
Sam