When induction doesn’t work (HSC SSCE Mathematics Extension 1): Flashcards
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Practise the cards
10 cards from this deck
What is the base case in induction proofs?
What is the base case in induction proofs?
The initial condition, usually n = 1.
What is the induction step?
What is the induction step?
Validates the hypothesis for n = k and k + 1.
What is a counter-example?
What is a counter-example?
An instance that refutes a proposition or conjecture.
Why do induction proofs fail?
Why do induction proofs fail?
Incorrect base case or flawed induction step logic.
How to verify base cases rigorously?
How to verify base cases rigorously?
Check the initial condition thoroughly to avoid errors.
What is a common mistake in induction proofs?
What is a common mistake in induction proofs?
Assuming P(k) without verifying all cases.
What happens if the base case is wrong?
What happens if the base case is wrong?
The entire induction proof may collapse.
What is a common mistake in induction proofs?
What is a common mistake in induction proofs?
Assuming the statement holds for n without proving it.
What is required for mathematical induction to work?
What is required for mathematical induction to work?
Base case and inductive step must be proven.
What should you do with flawed induction assumptions?
What should you do with flawed induction assumptions?
Use counter-examples to highlight limitations.