Numbers, Inequalities, Absolute Values

Question 1

Integer

Answer 1

…-3, -2, -1, 0, 1, 2, 3, 4, 5…

Question 2

Rational Number

Answer 2

r = m/n where m and n are integers and n does NOT = 0

Question 3

set notation

Answer 3

A set is a collection of objects, and these objects are called the elements of the set

Question 4

write in set-builder notation as

Answer 4

A = { x | x is an integer and 0

Question 5

Intervals

Answer 5

Certain sets of real numbers occur frequently in calculus and correspond geometrically to line segments.

Question 6

Rules for Inequalities

Answer 6

1. If a < b, then a + c < b + c
2. If a < b and c < d, then a + c < b + c
3. If a < b and c > 0, then ac < bc
4. If a < b and c < 0, then ac > bc
5. If 0 < a < b, then 1/a > 1/b

Question 7

Absolute Value

Answer 7

The absolute value of a number a, denoted by |a|, s the distance from a to 0 on the real number line. Distances are always positive or 0,

|a| >/ 0 for every number a

Question 8

Properties of Absolute Values

Answer 8

Suppose a and b are any real numbers and n is an integer. Then

1. |ab| = |a||b|
2. |a/b| = |a| / |b|
3. |a^n| = |a|^n

Question 9

The Triangle Inequality

Answer 9

If a and b are any real numbers, then

|a+b| /< |a| + |b|