EDMATH 304 - NUMBER THEORY

What is the first step in a proof by mathematical induction?

• Assume the result is true for some value

• Prove the result for the base case

• State the induction hypothesis

• Prove the result for the smallest value

In mathematical induction, what must be shown after proving the base case?

• The induction hypothesis is true.

• The result holds for an arbitrary value

• The result is true for all even numbers

• The result is true for some values

What is the purpose of the inductive step in mathematical induction?

• To prove the base case

• To disprove the result

• To extend the result to the next value

• To find the smallest value

Which of the following statements is true about mathematical induction

• It can only be used for odd numbers

• It is a form of trial and error

• It is a proof technique for proving statements about integers

• It is used for disproving mathematical statements

When proving by mathematical induction, what should be assumed for the inductive step?

• The statement is always false

• The statement is true for some arbitrary value.

• The statement is true for all values

• The statement is true for the largest value

In a proof by mathematical induction, what is the final step after proving the inductive step?

• State the base case.

• Conclude that the result holds for all values

• Prove the result for an arbitrary value.

• Assume the induction hypothesis

Which of the following is NOT a necessary part of a proof by mathematical induction?

• Proving the result for the base case

• Stating the induction hypothesis.

• Proving the result for the inductive step

• Assuming the result is true

What is the purpose of the base case in mathematical induction?

• To prove the result for the largest value

• To prove the result for an arbitrary value

• To state the induction hypothesis

• To establish the result for the smallest value

Which of the following is a common mistake when using mathematical induction?

• Proving the result for the base case only

• Assuming the result is true for all values

• Using an arbitrary value in the base case

• Skipping the inductive step

In a proof by mathematical induction, what is the role of the induction hypothesis?

• To state the smallest value

• To prove the result for the largest value

• To assume the result is true for some value

• To prove the result for all values