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# Algebra II Terms

### Algebra II Terms with definitions from MathWords.com

Whole number Non-negative integers {0,1,2,3,...}
Integer All positive and negative whole numbers. {...,-3,-2,-1,0,1,2,3,...}
Rational number All positive and negative fractions. Examples: -3, 11/3, 4.5, -6 2/5
Irrational number Any number that cannot be expressed as a fraction. Examples: e, pi
Domain The set of values of the independent variable for which a function or relation is defined. x-values
Range The set of values assumed by a function or relation over all the permitted values of the independent variable. y-values
Discrete A set with elements that are countable(i.e. you know what comes next in the set)
Continuous An interval of connected numbers. Example: 3<x<8
Real numbers All the numbers on the number line, including rational and irrational numbers.
Inequality 1: Any of the symbols <, >, ≤, or ≥. 2: A mathematical sentence built from expressions using one or more of the symbols <, >, ≤, or ≥.
Set A group of numbers, variables, geometric figures, or just about anything. Sets are written using set braces {}. For example, {1,2,3} is the set containing the elements 1, 2, and 3.
Set Braces The symbols { and } which are used to indicate sets.
Interval The set of all real numbers between two given numbers. The two numbers on the ends are the endpoints. The endpoints might or might not be included in the interval depending whether the interval is open, closed, or half-open (same as half-closed).
Interval notation A notation for representing an interval as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included.
Open Interval An interval that does not contain its endpoints. Example: (3, 8)
Closed Interval An interval that contains its endpoints. Example: [3,8]
Half-Open Interval An interval that contains one endpoint but not the other. Example: (3,8] or [3, 8)
Half-Closed Interval An interval that contains one endpoint but not the other. Example: (3,8] or [3, 8)
Exclusive Excluding the endpoints of an interval. For example, "the interval from 1 to 2, exclusive" means the open interval written either (1, 2).
Inclusive Including the endpoints of an interval. For example, "the interval from 1 to 2, inclusive" means the closed interval written [1, 2].
Set Builder Notation A shorthand used to write sets, often sets with an infinite number of elements.
Set Builder Notation (Abstract Example with verbal description) The set {x : x > 0} is read aloud, "the set of all x such that x is greater than 0." It is read aloud exactly the same way when the colon : is replaced by the vertical line | as in {x | x > 0}.
Set Builder Notation (Concrete Example with verbal description) the set of all real numbers except 3 {x: x ≠ 3}
Set Builder Notation (Concrete Example with verbal description) the set of all real numbers less than 5 {x | x < 5}
Set Builder Notation (Concrete Example with verbal description) the set of all real numbers greater than or equal to 0 {x2 | x is a real number}
Set Builder Notation (Concrete Example with verbal description) the set of all odd integers (e.g. ..., -3, -1, 1, 3, 5,...). {2n + 1: n is an integer}
Created by: shoemakers09