Question 1
In the context of induction, what is the base case?
Question 2
What can strengthen an inductive proof if you are stuck?
Question 3
Which base case is used in the proof that 3 divides n³ - n?
Question 4
In an example proof by induction of tiling a 2^n x 2^n courtyard with one missing square, which tile shape is predominantly used?
Question 5
What is the importance of ensuring diagrams are accurate in mathematical proofs?
Question 6
What is the first step in a proof by contradiction?
Question 7
In a direct proof, what should you start with?
Question 8
What must you show in the inductive step of a proof by induction?
Question 9
What logical contradiction arises from assuming √2 is rational?
Question 10
For the induction proof of the sum of natural numbers, what is P(n)?
Question 11
What should one ensure when using diagrams in proofs?
Question 12
What kind of numbers were the Pythagoreans troubled by when they discovered √2?
Question 13
What is the flaw in the false proof that 'all horses are the same color'?
Question 14
Which ancient society discovered the irrationality of √2?
Question 15
Which method uses the step-by-step deduction starting from an assumption that negates the desired conclusion?