When induction doesn’t work (HSC SSCE Mathematics Extension 1): Quizzes
📚Quizzes
Practise the questions
10 questions from this quiz
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Practise the questions
10 questions from this quiz
What does failure in induction often stem from?
What does failure in induction often stem from?
All of the above
Why is it important to verify the base case rigorously?
Why is it important to verify the base case rigorously?
To avoid initial errors
What can invalidate an induction proof?
What can invalidate an induction proof?
Assuming P(k) implies P(k+1) blindly
What is a common mistake when extending induction from P(k) to P(k+1)?
What is a common mistake when extending induction from P(k) to P(k+1)?
Skipping proof of P(k)
What should be checked to ensure the induction proof’s validity?
What should be checked to ensure the induction proof’s validity?
Both base case and step
Why might an induction proof be invalid even if the base case is correct?
Why might an induction proof be invalid even if the base case is correct?
Step logic is flawed
What does the phrase 'counter-example' mean in proofs?
What does the phrase 'counter-example' mean in proofs?
Refutes the hypothesis
In inductive proofs, what is a key to avoiding errors?
In inductive proofs, what is a key to avoiding errors?
Careful verification
What does the note suggest about induction as a proof method?
What does the note suggest about induction as a proof method?
Susceptible to errors
What is a crucial step in constructing a valid induction proof?
What is a crucial step in constructing a valid induction proof?
Verify base and induction step