ARITHMETIC GLOSSARY

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Title	Description
Additive Inverse for Arithmetic	The opposite of a given number. Change the sign of a number to have its additive inverse. The sum of a number and its additive inverse is always zero.
Additive Property of Equality	This property allows us to add equals to equals to stay equal. Given two equal values, we may add the same quantity to both values and retain an equality.
Arithmetic	A branch of mathematics built upon the basic operations of addition, subtraction, division, and multiplication. Powers, roots, and logarithms are often considered arithmetic in nature.
Associative Law of Addition	Provides that addition of groups of terms or values is indifferent to the order of grouping. We may add terms in any order, or group them in any order.
Associative Law of Multiplication	Provides that multiplication of groups of terms or factors is indifferent to the order of grouping. We may multiply factors in any order, or group them in any order.
Beta	Beta is the second letter of the Greek alphabet.
Braces	Braces act just like parentheses. Always (almost) used in pairs, braces look like this: { }.
Brackets	Brackets act just like parentheses, coming in pairs to group data or terms.
Cardinal Number	The number of objects or elements within a set is the Cardinal Number of the set.
Commutative Law of Addition	When adding terms the order in which we add them matters not at all.
Commutative Law of Multiplication	The order in which we multiply any number of factors (to obtain the product of those factors) matters not at all.
Countable	In common language, countable just means reasonably enumerated or countable, as in there are not too many objects to physically count. In human terms, the grains of sand in the Sahara Desert are not countable. But mathematically they actually are. So Countable means something a little different to the mathematicians.
Counting Numbers	The set of Counting Numbers is (usually) identical to the set of Natural Numbers, the positive integers that we begin to count with when we're little kids. Watch out, however: some people include zero in this set.
Cube Root	The Cube Root of a real value is the number that when raised to the third power equates to the original real value.
Denominator	The Denominator of a fraction is the number on the bottom; it is the divisor of the numerator.
Difference	The result of subtraction is often considered a Difference.
Digit	Each of the numerals 0 through 9 is a Digit. The term also refers to place value, as the "tens digit" or the "hundredths digit."
Dividend	When we divide, we typically "begin" with a dividend. We divide the dividend by the divisor and we get the resulting quotient. In a fraction, which is always top-divided-by-bottom (numerator divided by denominator), the top of the fraction is the dividend, the bottom is the divisor, and the value of the resulting fraction is the quotient.
Divisor	The number we "take into" the dividend when we divide is termed the Divisor. In fractions, which are always top-divided-by-bottom (numerator divided by denominator) we divide the top (the dividend) by the bottom (the divisor) and the value of the resulting fraction is the quotient.
Double	Twice the value of a real number is Double the value. To Double is to multiply by two, so to Double a half results in a whole.
Equal	In the United States all men are created Equal, endowed by their Creator with certain unalienable rights that include life, liberty, and the pursuit of happiness.
Equality	A statement where two or more values are deemed to have an equal or identical value is a statement of Equality.
Even (integer)	Even integers end with one of the following five digits: 0, 2, 4, 6, or 8. These digits are considered Even and the integers that end with them are also considered Even. When Even integers are divided by two the quotient is an integer.
Fraction	Fractions are many, many things. But always, without fail, fractions are the result of dividing the top value (numerator) by the bottom value (denominator).
Fundamental Theorem of Arithmetic	A theorem that all integers can be written as the product of prime numbers is often called the Fundamental Theorem of Arithmetic.
Googol	Ten raised to the power of one hundred equals one Googol.
Googolplex	Ten raised to the power of a googol is a Googolplex; it is a huge number.
Greatest Common Factor	The GCF of two integers (usually) is the largest integer that divides evenly into both integers. We sometimes use GCF for non-integral values.
Height	Altitude. How tall something is, measured in some perpendicular fashion to the "bottom" is its height.
Horizontal	Horizontal comes from orientation like the horizon; parallel to the "flat" surface of the earth; perpendicular to vertical.
Hypotenuse	The longest side of a right triangle is the Hypotenuse; it is always opposite the 90-degree angle (or right vertex).
Identity Property of Addition	The Identity Property of Addition says that adding zero to (or subtracting zero from) any real value will not change the value.
Identity Property of Multiplication	The Identity Property of Multiplication says that multiplication of a real value by one (or division by one) will not change the value.
Impossibility	Despite what some "possibility thinkers" espouse, some things are mathematically impossible. For example, an exact real number cannot be simultaneously irrational and rational.
Increasing	If the values in the range of a function increase as the values of the domain increase, the function is said to be Increasing.
Inequality	Generally of one of the following four forms: less than, less-than-or-equal-to, greater than, or greater-than-or-equal-to.
Infinite	In common language, not countable in any practical manner. In math, having no bounds or boundary.
Infinitesimal	Infinitely small is Infinitesimal, so tiny that it occupies no space. While in human terms anything really small (a molecule) is Infinitesimal, in math the term means approaching zero in size.
Infinity	That without bound; limitless.
Integer	An Integer is a whole number or its negative. When expressed as a decimal, an Integer has nothing to the right of the decimal point (in American style).
Interest	Given the time-value-of-money, Interest is generated on a sum of capital as time passes.
Interior	Interior means within or "in-between."
Intersection	Where geometric entities cross, or where sets have common elements, is termed an Intersection.
Irrational Number	An Irrational Number cannot be expressed exactly as the ratio of two integers. Irrational Numbers, when expressed as decimals, never repeat or terminate.
Least Common Denominator	When two or more fractions are being summed we want the LCD to facilitate the operation of addition.
Least Common Multiple	The LCM is most typically applied to integers. It is the smallest value evenly divisible by each number for which we seek the LCM.
Line Segment	A section of a line, with endpoints on both ends, is a Line Segment.
Logic	Logic takes many forms and is instrumental in understanding the language of mathematics.
Long Division	Adolph Hitler actually had two middle names: Long Division. Just kidding. And we should not kid about an evil, pestiferous maniac like Hitler.
Magnitude, Powers of Ten	Often when we compare the multiplication by various powers of ten we speak of the magnitude of the effect of the multiplication.
Measure	A noun or verb, Measure implies comparison to an established standard.
Measurement	The result from comparison to an established standard, Measurement may be exact only to an agreed-to precision.
Minimum	A low point or least value in the neighborhood of the graph of a function is a Minimum, the singular of minima.
Minute, Time	One-sixtieth of an hour comprises one Minute of time.
Mixed Number	We may write an "improper" fraction as a whole number followed immediately with a "proper" fraction. Such a form is termed a Mixed Fraction.
Mode	While Mode can take on several meanings in mathematics, it generally is used for the value of data with the greatest frequency of occurrence in a list of values.
Multiplication	You know, times. The operation to simplify addition of identical values. You should learn your Times Tables, the basic facts of Multiplication.
Multiplicative Inverse	Another name for Multiplicative Inverse is reciprocal. Reciprocals multiply to one.
Natural	The set of Natural Numbers is also the set of counting numbers, the same numbers we learn to count when we're little kids: 1, 2, 3, 4.... Precisely in the language of math these are the positive integers.
Natural Numbers	The set of Natural Numbers is also the set of counting numbers, the same numbers we learn to count when we're little kids: 1, 2, 3, 4.... More precisely in the language of math these are the positive integers.
Negative	Real values less than zero are Negative. We also consider the Negative of a real value to have the opposite sign, as the opposite (or Negative) of a Negative value is positive.
Negative Number	A real value less than zero is a Negative Number.
Negative Reciprocal	The product of two Negative Reciprocals is -1. When lines in Cartesian or rectangular coordinates meet at right angles they have Negative Reciprocal slopes, unless they are precisely horizontal and vertical.
Nonnegative	We have occasions to refer to all positive values as well as to zero. These are all the real values that are Nonnegative. Literally, not negative.
Nonzero	Literally, not zero. Typically used to mean either positive or negative values.
Nth Degree	Simply raised to the degree of integer (usually) n, or N. In common, everyday language, to pursue something excessively, as parents giving the suitor of their teenage daughter an interrogation "to the nth degree."
Nth Root	Given some integer N and a real value, the Nth Root of the real value is the number that when raised to the N power returns the real value.
Null Set	The Null Set is the empty set. Mathematically there is but one empty set, the unique Null Set, the set with nothing in it.
Number Line	The real Number Line is a depiction of the set of all real numbers from negative infinity to positive infinity. All real numbers lie on the Real Number Line.
Numerator	The top number in a fraction, above the fraction bar, is the Numerator. It is the dividend to be divided by the divisor, which is the denominator.
Octagon	An eight-sided polygon.
Odd	In common language: strange or unusual. For integers, numbers ending with any of these digits: 1, 3, 5, 7, or 9.
One-Dimensional	Linear, or along one line of direction. Informally, constrained to stay along a narrow line.
Operation	The processes of addition, subtraction, multiplication, and division are each termed an Operation. So, too, is raising a value to a exponent.
Opposite	Many meanings are found for Opposite, including having direction 180 degrees from an original direction, or having the negative sign of a previous sign. Opposite real values have identical absolute values.
Order of Operations	We have a hierarchy of Order to Operations in the language of mathematics. We do multiplication before we do addition, and we also work left-to-right. We work first inside of expressions within parentheses, then outward.
Ordered Pair	Two coordinates are required to label a point in a plane, typically (x, y).
Ordered Triple	Three coordinates are required to label a point in space, typically (x, y, z).
Ordinal Number	Ordinal Numbers are ordinary numbers, or the sequential references of order as first, second, third, and so on.
Ordinate	In Cartesian or rectangular coordinates, the y-axis, or the coordinate from the y-axis; the second coordinate in an ordered pair.
Origin	In one dimension: (0). In two dimensions: (0,0). In three dimensions: (0, 0, 0).
Outlier	When plotting data points, as in a scatterplot, if a single data point is far removed from the neighborhood of the other data points, such a far-removed data point is called an Outlier.
Oval	In common language, any elliptical shape or not-quite round "circular" shape is called an Oval. Mathematically, an ellipse is not an Oval.
Parentheses	Symbols ( ) serve to isolate or group written entities.
Pentagon	A five-sided polygon.
Percent	Literally, per hundred.
Percentage	Any reference to percent is a Percentage; the fraction of 100 a value represents.
Percentile	Certain types of data lend themselves to description by what percent of the values exceed (or fall below) a specific data value. A Percentile states what percent of the data is less than the specific data value.
Perfect Square	Most generally a Perfect Square is an integer that is the product of another integer times itself.
Perimeter	The distance around the outside of a planar object or a plane figure is its perimeter.
Perpendicular	At right angles.
Phi	The twenty-first letter of the Greek alphabet.
Pi	The constant ratio of circumference to diameter is represented by the 16th letter of the Greek alphabet; it is approximately 3.14159.
Plane	An infinite expanse of points in two dimensions.
Plus	A symbol for addition, or the operation itself.
Point	A location of infinitesimal size, that is, no size. A mathematical idea.
Positive	Real values are Positive when they are greater than zero.
Power	Power most often means the value of an exponent.
Precision	The quality of finer measurement or estimation is termed Precision.
Prime Factorization	The process of finding the prime factors of a composite number is called Prime Factorization.
Prime Number	A positive integer evenly divisible by itself and one but no other integers is considered a Prime Number.
Principal	An amount, typically money, upon which the time value of money (accumulation of an added percentage over a defined time) generates interest is termed Principal.
Probability	The likelihood of an event or particular outcome is its Probability. All Probabilities are between 0 and 1 (between zero percent and 100 percent).
Product	The result of the operation of multiplication is called a Product.
Proper Subset	A set that is a subset of a given set and not identical to the given set is a Proper Subset of the given set.
Proportional	In a (constant) ratio.
Psi	The 23rd letter (next-to-last) of the Greek alphabet.
Pythagorean Triple	A series of three integers for whom the Pythagorean relation holds, as 3-4-5 or 5-12-13, because 3² + 4² = 5² and 5² + 12² = 13².
Quadrangle	Another name for a quadrilateral, a four-sided polygon.
Quadruple	A verb or noun; to multiply by four or the fourth integral multiple, respectively.
Quartiles	Most generally, the 25th and 75th percentiles are termed the Low Quartile and High Quartile, respectively.
Quintiles	Most generally, the 20th and 80th percentiles are termed the Low Quintile and High Quintile, respectively.
Quintuple	A verb or noun; to multiply by five or the fifth integral multiple, respectively.
Quotient	The result of the operation of division, the Quotient results from dividing a dividend by a divisor; also the value of a fraction that is always numerator divided by denominator.
Radical	A root symbol or the root itself is sometimes termed a Radical.
Radicand	A number taken to a root is a Radicand; the number under a root sign.
Radius	One-half the diameter of a circle is the Radius. It is the distance from the center of a circle to any point on the circle.
Range	We may speak of a Range of values as simply the difference between high and low values of a data set. More specifically, the values generated by the input of domain values into a function map into the Range of values of the function.
Ratio	Sometimes Ratio is meant to state a constant proportion. More generally, the Ratio of two real values is the quotient of one number divided by the other.
Rational	A Rational number can be expressed as the ratio of two integers. When expressed as a decimal, a Rational number will either repeat or terminate (with repeating zeros).
Rational Expression	Mathematical statements written as fractions with a numerator and a denominator are often termed Rational Expressions.
Ray	A set of collinear points, a Ray has an endpoint and proceeds infinitely far in a single direction.
Real Number	Depicted on the Real Number line, such a value is either less than, equal to, or greater than every other real value.
Reciprocal	Every nonzero real value has a Reciprocal. A number and its Reciprocal multiply to one. We may find a Reciprocal of a number by dividing it into 1.
Rectangle	A quadrilateral with many special properties, including all those of a parallelogram, and then some.
Relatively Prime	Two integers with no common factors other than one are said to be Relatively Prime.
Remainder	When a divisor does not divide evenly into the dividend, we have a Remainder.
Right Angle	An angle of 90 degrees or pi/2 radians. Perpendicular lines meet at Right Angles.
Right Triangle	A triangle with a right angle.
Root, Number	The Root of a given Number is the value that raised to the power of the root returns the given number.
Rounding	Not exactly truncating, rounding involves reduction in the precision of a value to approximate that value to some exact value with less precision.
Sample	When we Sample a population we typically seek a representative Sample.
Scientific Notation	Scientific Notation is a way to easily represent values far from zero, in terms of powers of ten, either very large numbers or very small numbers; they are usually representative of physical quantities or values.
Second, Degree	While "second degree" applies to a polynomial, a single Second with respect to Degree measure is one-sixtieth of one minute, or one sixtieth of one sixtieth of one degree, or 1/1,296,000 of a revolution.
Second, Time	One sixtieth of a minute, or 1/3600 of an hour, is one Second of Time.
Segment, Circle	A portion of a circle bounded by a chord and the circle itself.
Segment, Line	A Line Segment is a set of collinear points bounded on both ends with, literally, endpoints.
Semicircle	Half a circle; the portion of a circle on one side of a diameter.
Set	Any collection of objects or values is considered a Set, whose cardinal number is the number of objects in the Set.
Significant Digits	Informally, Digits that are not zero. Slightly more formally, nonzero Digits as well as zeros between nonzero Digits. Strictly, the number of Digits required to express a calculated value to within the reasonable tolerance or uncertainty of calculation.
Simplify	When we Simplify mathematical expressions we restate them (or rewrite them) in more concise terms.
Solution	Too often in math class, "the answer." More directly, a Solution is a value (or set of values) that makes a mathematical statement true.
Solution Set	Strictly, any Solution is a Solution Set, the value(s) that make a mathematical statement true.
Speed	A (typically fixed) ratio of length or distance to a unit of time; Speed is a scalar value, as in miles per hour (mph) or feet per second (fps).
Square	One noun: the regular quadrilateral, equilateral and equiangular. Another noun: the result of multiplying a number times itself. Or, the verb: the operation of multiplying a number times itself, equivalently raising it to power two.
Square Root	Given a real value, the number that times itself (squared) produces the given value is its Square Root
Stem-and-Leaf Plot	A graphical device to group statistical data, typically by leading digits.
Strict Inequality	A Strict Inequality does not include an "or equal to..."
Subset	Every set is a Subset of itself. A Subset has elements all contained in a "parent" set.
Subtraction	The operation we begin thinking of as "take away" or "minus" is a way to find the difference between values.
Sum	The result of addition.
Three Dimensions	The Dimensions of space or volume are Three Dimensions, typically labeled with rectangular, spherical, or cylindrical coordinates.
Triangle	A three-sided polygon. Triangles are either acute, right, or obtuse.
Triple	As a verb, Triple means to multiply by three. As a noun, the result from multiplication by three.
Truncation	Replace the lesser digits of some number with zeros with no regard for rounding; this is Truncation.
Two Dimensions	A plane has Two Dimensions. Planar figures are Two Dimensional.
Uniform	Constant and unchanging; fixed.
Union	The Union of two or more sets is the set of elements from all the sets. The Union of sets A and B is literally the set "A and B."
Velocity	Formally a vector in physics, Velocity has both magnitude (speed) and direction.
Venn Diagram	Most often graphics of overlapping circles and ovals, a Venn Diagram depicts sets, subsets, and their intersections and unions.
Vertex	A "corner" of a polygon is a Vertex; an extremum of a conic section is a Vertex; the endpoint(s) of rays that form an angle is a Vertex.
Vertical	Straight up, perpendicular to horizontal, is Vertical. Vertical lines have an indeterminate or infinite slope.
Weighted Average	When several factors comprise a score or calculation and the factors have different amounts of importance to the overall result, a Weighted Average may be calculated by assigning more importance (or "weight") to one factor over another.
Zero	The only real value that is neither negative nor positive. It is an integer value.

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