Proof
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1
What is a set?
a collection of objects or numbers called elements, shown using curly brackets
2
How is a set often represented?
by a capital letter, e.g., A = {0, 1, 2}
3
What are three ways to write sets?
a list of elements, a rule, mathematical notation
4
What does the symbol p → q mean?
p implies q or if p then q
5
What does p ⇔ q signify?
p implies q and q implies p (p if and only if q)
6
What does the symbol ≠ represent?
not equal to
7
What does ≈ mean?
approximately equal to
8
What does the identity symbol (=) signify?
two things are identically equal to each other
9
What is proof by exhaustion?
a method where you break things down into 2 or more cases to prove a statement
10
In the proof example, what are the two cases for x?
x is an even number and x is an odd number
11
How can an even integer x be expressed?
as x = 2n for some integer n
12
What does f(2n) equal when x is even?
2(4n³ + n) + 1
13
How can an odd integer x be expressed?
as x = 2m + 1 for some integer m
14
What does f(2m + 1) equal when x is odd?
2(4m³ + 6m² + 4m + 1) + 1
15
What can be concluded about f(x) for any integer?
f(x) is odd for any integer
16
What is the result of (n + 6)² - (n + 1)²?
5(2n + 7)
17
If n is an integer, what else is 2n + 7?
also an integer
18
What does it mean if (n + 6)² - (n + 12) is divisible by 5?
it can be divided by 5
19
What does (x + 2)(x - 1) > x² - 2 represent?
a mathematical inequality to check
20
What happens when x = 1 in the inequality?
the statement is false because 0 > 0 is not true
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