Topic explanation

Standard explanation

Assume P(k), multiply both sides by a positive number, or add a positive term. Track the direction of >= . Base often n=1 or n=2 as stated.

Key points

• keep the inequality direction
• write the k+1 expression in terms of the k piece
• leftover must be divisible / positive
• split into IH piece + 3
• INDUCTION ON INEQUALITIES: Assume P(k), multiply both sides by a positive number, or add a positive term. Track the direction o
• INEQUALITIES: Assume P(k), multiply both sides by a positive number, or add a positive term.
• WHAT — INDUCTION ON INEQUALITIES: Assume P(k), multiply both sides by a positive number, or add a positive term. Track the direction o
• WHY — Why it matters: This rule is a separate learning unit inside induction on divisibility and inequalities. It can be d

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