Mathematics Glossary N-Z

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Term
Definition
N
Natural Numbers 
N 
{1,2,3,...}
Negation
~ 
The negation of a statements is false when the statement is true, and true when the statement is false. The meaning here is NOT or THE OPPOSITE OF.
Newton's Method

Newton's method for estimating the roots of polynomial functions:
Noncollinear
Points which do not all lie in a straight line.
Null Set
{} 
A set with no contents. (See Empty Set)
O
One-to-one
A function or relation is one-to-one if no two points in the function have different x-coordinates and the same y-coordinates. (This function then passes a horizontal line test.
Open Interval
An Interval which does not include either endpoint . Another way to write this interval above is: (a,b0. The "rounded" parentheses indicate that a and b are not to be included.
Open Sentence
Sentences (equations) that have variables to be replaced. Open sentences cannot be labeled as true or false, their status is "open."
Ordered Pair (a,b) A set of two numbers, with the x-coordinate (independent variable) listed first, and the y-coordinate (dependent variable) listed second.
Order of Operations
The order in which  mathematical operations must be done. 
 
Abbr.
Memory
Represents
Rank
P 
Please 
Parentheses 
1 
E 
Excuse 
Exponents 
2 
M 
My 
Multiplication 
3
D 
Dear 
Division 
3
A 
Aunt 
Addition 
5
S 
Sally 
Subtraction 
5
In case of a tie, work from left to right.
P
Paradox
A sentence which contradicts itself. (Ex.: This statement is false.)
Parallel
Two or more lines that never intersect. Their slopes are exactly equal.
Parameter
A third variable which x and y are described in terms of. (t is a frequently used parameter representing time.
Parametric Curve
A Cartesian graph or curve represented by two parametric equations.
Parametric Equations
Two equations, each representing the x and y coordinates of a Cartesian graph expressed in terms of a third variable, or parameter.
Perfect Square Trinomials
Perpendicular
Two lines that form a right angle (90 degrees). Their slopes are negative reciprocals of each other. (The product of their slopes is -1)
Polynomial
An algebraic expression with more than one term (monomial)
Power Function
A function where the independent variable is the base and constant is the exponent. , where x is the independent variable and c is the constant, and is a positive integer.
Product Rule
(for derivatives)
The derivative of a product is the first function multiplied by the derivative of the second function plus the second function multiplied by the derivative of the first fuction. In symbols, this is shown below:
Proper Subset
a subset of, but not equal to the other set.
Properties
Principles or rules that mathematics always follows.
Pure Imaginary Numbers
For any positive real number b,  where i is the imaginary unit, and bi is called a pure imaginary number.
Q
Quadratic Equation
A quadratic equation is an equation of the form: , where a, b, and c are real numbers with a0. (The degree of the equation is 2) (The highest exponent of a variable is 2)
Quadratic Formula
Given a quadratic equation in the form: , and that  ,then the solutions of the equation will always be: .
Quadrant
The x-axis and y-axis separate the plane into four regions called quadrants. They are numbered with Roman numerals, beginning in the upper right quadrant and proceeding in a counter-clockwise rotation.
Quotient Rule
The derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator. In symbols, this is shown below:
R  
Rational Function
A ratio of two polynomial functions, , where .
Rational Numbers
Q 

Decimal Form: repeater or terminator 
Range
The set of all y coordinates in a relation.
Real Numbers 

 
R 
Reciprocal
The number which when multiplied by a given number results in the Multiplicative Identity (1). 
(See Multiplicative Inverse)
Reflecting Transformation
A modification of a function which causes the function to be reflected about the x-axis or y-axis. reflects the graph of  about the x-axis.  reflects the graph of  about the y-axis.
Reflexive Property (of equality)
For any real number a, a = a
Relation
Any Set of ordered pairs.
Relative Maximum
The maximum value of the function near a specified value in the domain.(See Local Maximum)
Relative Minimum
The minimum value of the function near a specified value in the domain. (See Local Minimum)
Removable Discontinuity
A discontinuity at a point which could be removed by defining the function at just that one point. This often appears as a graph with a hole in it. Here is an example:
Riddle I (factoring)
Riddle II (factoring)
Right-Hand Limit
A function is continuous from the right if (This is called a right-hand limit.
Root Function
An exponential function where  with n being an integer. This can also be stated as.
Row Matrix
A matrix with only 1 row.
S
Scalar
In the context of a matrix problem, a scalar is a non-matrix, "normal" number.
Scalar Multiplication
the scalar  is multiplied by each element of the matrix.
Scatter Plot
The plotting of scientific data with two variables.
Scientific Notation
A number with the decimal point after the first nonzero digit multiplied by 10 to the appropriate power.
Secant
A line which intersects a curve in two points.
Set
A collection of items (elements) or objects 
Simple Statement
A single statement.
Slope
The steepness of a line. The ratio of the vertical change to the horizontal change. The average rate of change over an interval.
Solution
A replacement (substitution)  for the variable that will make the equation true.
Square Matrix
A matrix with the same number or rows as columns.
Statement
A declarative sentence that can be classified as true or false but not both simultaneously. (This is an exclusive OR)
Stretching Transformation
A modification of a function which causes the function to be "stretched out" vertically or horizontally. In the function , a can "stretch" (or shrink) the sine function. If a is negative, it also causes the function to be inverted.
Subset
A set, all of whose elements are also elements of the other set
Substitution Property
if  then either can be substituted for either at any time
Subtraction of Functions
. he domain for this combination function is , where A is the domain of function f, and B is the domain of function g. Example if:  and , then 
Sum of Two Cubes
Symmetric Property 
(of equality)
For all real numbers a and b, if a = b, then b = a
T
Tangent
A line or segment which intersects a curve in only one point. In both examples below line l is tangent to the curve. Even though the second illustration shows the line intersecting the curve in more than 1 point, "locally" around point P, there is only one point of intersection. This is a special relationship because a line could easily intersect a curve iin zero or two points. Tangency is special with the touching at only one point.

Term
An expression that is a number, a variable, or the product of a number and one or more variables. Also called a monomial.
Terminal Point
The terminal point of a parametric curve is the point which represents the x and y values when the parameter takes on the greatest value in its domain.
Transitive Property (of equality)
For all real numbers a, b, and c, if a = b and b = c, 
then a = c.
Trichotomy Property
For any real numbers a and b, either 
1)a<b, or 2)a=b, or 3)a>b
Trigonometric Function
A function which includes algebraic operations and any of the six trigonometric definitions. (sine, cosine, tangent, cosecant, secant, cotangent). Example: 
Transcendental Function
A function that is not algebraic. This includes trigonometric, inverse trigonometric, exponential, and logarithmic functions. Example: 
Translation
A modification of a function which causes the entire function to be moved or "translated" horizonatlly from its orginal position. Depending on the value of h in the following function, f(x) will be translated left or right. If h=2, then f(x) will be translated 2 units to the right. If h=(-1), then f(x) will be translated 1 unit to the right. 
Truth Table
A table of all possible outcomes of a symbolic statement.
U
Union
The joining of sets into a master set. Union will not yield multiples of the same item
Universal Set
U
The set of all elements under discussion.
V
Variable
A symbol that represents an unknown quantity.
Vertex (geometry)
Endpoints of a line segment. (Plural: vertices)
Vertex (networks)
Endpoints of arcs.
Vertical Line Test
A test which takes a vertical line at any horizontal position. If at any position there is a crossing at more than one point, then the relation fails the Vertical Line Test, and the relation is not a function.
W
Whole Numbers
W 
{0,1,2,...}
X
X-Axis
The horizontal reference line in the Coordinate Plane.
X-Coordinate
The first coordinate in an ordered pair. This represents the independent variable.
X-Intercept
The point where a graph intersects the x-axis.
Y
Y-Axis
The vertical reference line in the Coordinate Plane.
Y-Coordinate
The second coordinate in an ordered pair. This represents the dependent variable.
Y-Intercept
The point where a graph intersects the y-axis.
Z
Zero Product Property
When ever you have a product which is set equal to zero, then each and every factor can cause the product to be zero.  (or any combination thereof)