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Variable

an alphabetic character representing a number, called the value, which is either arbitrary or not fully specified or unknown. It is usually a letter like x or y.

Sentence

Two algebraic expressions connected by =, not equal to, <, >,

Equation

A mathematical sentence that contains an equals sign

inequality

A mathematical sentence that shows the relationship between quantities that are not equivalent

Open sentence

An equation or an inequality that contains an algebraic expression

Solution

The value or values that make an equation or inequality true.

Set

A _ is a well-defined collection of objects.

Elements (or members)

Single item in a set

Equal sets

Sets are equal if and only if they have the same elements.

Whole numbers (or W)

{0, 1, 2, 3, ...}

Integers (I)

The whole numbers and their opposites. {0, ±1, ±2, ±3,...}

Real numbers (designated with a script R)

The set of all numbers than can be represented as repeating, terminating, or non-terminating decimals. All the numbers you currently know are real.

Domain

The ______________________ is all the possible INPUT, X, values.

solution set

The set of values that make a statement true.

Intervals

Literally "between values". An interval is a set of numbers between 2 numbers a and b and possibly including a, or b, or both.

Endpoints

The numbers a and b from the interval.

Open interval

An interval that does NOT include the endpoints. For example 0 < w < 6. (Has no = signs included.)

Closed interval

Both endpoints are included. 0 ≤ w ≤ 6. (Has = sign included at both ends.)

intersection

The graph of a compound inequality with "and" in which the solution is the overlapping or what is shared.

union

The graph of a compound inequality with "or" in which the solution is all points that satisfy one or the other or both inequalities.

Empty Set

Represents the set with no elements in it, the set symbol the 0 with the / through it represents the Empty Set

Numerical expressions

An expression which does NOT contain a verb and combines numbers only

Algebraic expressions

An expression which does NOT contain a verb, but DOES contain at least 1 variable.

Evaluating

Finding the value of an expression

Formula

An equation that relates two or more quantities

Square Root

when multiplying a number by itself to get a square number

√

Radical sign. Acts as a grouping symbol, so must evaluate under the sign first.

Radicand

The numbers under the radical sign 7.1

Square of the Square Root Property

√n • √n = n. When you square a square root, the answer is the radicand.

Every positive number has TWO square roots, one positive and one negative.

a = b², then b = ± √a for every b > 0.

Perfect squares

Squares of whole numbers