Lesson subsection
Read the explanation, try the on-paper prompts, then explain the idea in your own words. Use AI feedback as a mentor, not a shortcut.
Best flow: read → think on paper → write a short explanation → refine with feedback.
Many induction mistakes come from subtle logical or algebraic errors.
Common pitfalls:
Forgetting the base case. Without a base case, the "domino chain" never starts.
Using P(k + 1) in the induction step. You may only assume P(k), not what you're trying to prove.
Incorrect algebra when going from k to k + 1. Sloppy manipulation can completely break the proof.
Not clearly stating the induction hypothesis. You should explicitly say: "Assume P(k) holds for some k ≥ n₀."
Assuming the result for all smaller values without saying strong induction is used.
Good habits:
TL;DR — key idea
Most induction errors come from missing base cases, misusing the induction hypothesis, or hiding key steps. Clear structure and explicit hypotheses fix most of them.
Don’t skip this – writing proofs or explanations on paper is where most of the learning actually happens.
Write P(n) explicitly for one induction problem you've solved (or from this module). Then: 1. Write a correct base case. 2. Write a precise induction hypothesis. 3. Identify exactly one line in your proof where you *use* the hypothesis. Reflect on whether any of your past proofs accidentally committed one of the listed pitfalls.
Once you’ve sketched some ideas, summarize the main insight in the reflection box on the right.
In 3–6 sentences, explain the core idea of this subsection as if you were teaching a friend who hasn’t seen it. Focus on the logic, not just the final statements.
AI is optional. Use it to spot gaps and sharpen your wording, not to replace your own thinking.