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Mathematical Induction Quiz

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1. What is the first step in proving a statement using mathematical induction?

2. In the context of mathematical induction, what is the purpose of the induction step?

3. Which of the following is an example of a statement that can be proven using mathematical induction?

4. What must be true for a mathematical induction proof to be valid?

5. How does the principle of mathematical induction relate to well-ordering principle?

6. Which of the following is NOT a common use of mathematical induction?

7. When conducting a proof by induction, what is assumed in the induction hypothesis?

8. Which of the following statements about mathematical induction is TRUE?

9. Why is the assumption in the induction step ($n=k$ to $n=k+1$) crucial for mathematical induction?

10. In mathematical induction, the statement 'For all natural numbers $n$, if $P(n)$ is true, then $P(n+1)$ is also true' primarily refers to which part of the proof?