Chapter 1.2: Algebraic Expressions and Sets of Numbers

Vocabulary flashcards covering core algebraic concepts, sets of numbers, set-builder notation, and real number properties.

Variable

A letter used to represent any number.

Algebraic Expression

An expression formed by numbers and variables connected by the operation of addition, subtraction, multiplication, division, raising to powers, and/or taking roots.

Evaluating Algebraic Expressions

The process of substituting the numerical value for each variable into the expression and simplifying the result.

Number Line

A line on which each point is associated with a number.

Natural Numbers

The set of numbers $\{1, 2, 3, 4, 5, 6 \dots\}$.

Whole Numbers

The set of numbers $\{0, 1, 2, 3, 4 \dots\}$.

Integers

The set of numbers $\{\dots -3, -2, -1, 0, 1, 2, 3 \dots\}$.

Ellipsis

A symbol consisting of three dots that means to continue in the same pattern.

Set Builder Notation

A notation that describes the members of a set, but does not list them.

Empty Set (or Null Set)

A set that contains no elements, symbolized by $\{\}$.

Real Numbers

The set defined as $\{x \mid x \text{ corresponds to a point on the number line}\}$.

Rational Numbers

The set defined as $\{\frac{a}{b} \mid a \text{ and } b \text{ are integers and } b \neq 0\}$.

Irrational Numbers

The set defined as $\{x \mid x \text{ is a real number and } x \text{ is not a rational number}\}$.

Absolute Value

The distance between $a$ and $0$ on the number line for a real number $a$, denoted by $|a|$.

Opposite

The number $-a$ for a given number $a$.

Double Negative Property

The property stating that for every real number $a$, $-(-a) = a$.