The discussion revolves around proving the theorem "If m divides n, then m <= n" using various methods such as direct proof, mathematical induction, contraposition, or contradiction.
Some participants provide insights and clarifications, suggesting that if k is greater than 1, it implies certain relationships between m and n. There is an acknowledgment of confusion and a collaborative effort to clarify the logical steps involved in the proof.
Participants express uncertainty about how to proceed with the proof after establishing the equality case, indicating a need for further exploration of the implications of k's value.
SurferStrobe said:Homework Statement
Prove a theorem using direct proof, mathematical induction, contraposition, or contradiction.
Homework Equations
"If m divides n, then m <= n."
The Attempt at a Solution
(a) Suppose m divides n, then m = nk for some integer k.
(b) If k = 1, the m = n(1) = n.
That show equality part. How do I now show inequality? I'm at a loss for the next step.