Floor and Ceiling
⌊3.9⌋ + ⌈2.1⌉ = ?
What is 3 + 3 = 6?
Solve: |x - 3| = 5
What is x = 8 or x = -2?
The first step in a mathematical induction proof.
What is the base case?
Compute 3!
What is 6?
Compute 7 mod 3.
What is 1?
⌈-4.3⌉ + ⌊-4.3⌋ = ?
What is (-4) + (-5) = -9?
True or False: The absolute value function is always positive.
What is False? (It can be 0)
True or False: Induction proves a statement for all integers.
What is False? (Only for natural numbers or a given range)
Find 8!/6!
What is 56?
4! = ?
What is 24?
If ⌊x + 2.7⌋ = 6, what is a possible value of x?
What is 3.3 ≤ x < 4.3?
If |a - b| = 3 and a = 8, find b.
What is b = 5 or b = 11?
The second step in induction assumes P(k) is true. This is called the ______.
What is the inductive hypothesis?
True or False: n! = n × (n-1)!
What is true?
Compute (15 mod 7) + (8 mod 5).
What is 1 + 3 = 4?
f ⌊x⌋ = 7, what is a possible value of x?
What is any number 7 ≤ x < 8?
Solve: |x + 2| - |x - 2| = 4
What is x > 2?
What is (n(n+1))/2?
Evaluate: (7! / 5!)
What is 42?
Solve: |2x - 4| = 10
What is x = 7 or x = -3?
Solve for x: ⌈x⌉ = 5 and ⌊x⌋ = 4.
What is 4 ≤ x < 5?
Solve for x: |2x - 5| = |x + 1|
What is x = 6 or x = 2?
This step shows that if true for n = k, it must be true for n = k+1.
What is step 3 or the inductive step?
Compute the last digit of 9!
What is 0?
The ratio (n+1)!/n! simplifies to this equation.
What is n+1?