Math Glossary: Mathematics Terms and Definitions
Numbers, symbols and operators (such as + and ?) grouped together that show the value of something. Examples: • 2 + 3 is an expression. • 3 ? x/2 is also an expression. Algebra - Definitions. An expression is a sentence with a minimum of two numbers and at least one math operation. This math operation can be addition, subtraction, multiplication, and division. The structure of an expression is: Expression = (Number, Math Operator, Number).
In mathematicsan expression or mathematical expression is a finite combination of symbols that is well-formed according des rules that depend on the context. Mathematical symbols can designate numbers constantsvariablesoperationsfunctionsbracketspunctuation, and grouping to help determine order of operationsand other aspects of logical syntax.
Many authors distinguish an expression from a formulathe former denoting a mathematical object, and the latter denoting a statement about mathematical objects. However, in modern mathematics, and in particular in computer algebraformulas are viewed as expressions that can be evaluated to true or kathematicaldepending on the values that are given to the variables occurring in the expressions.
An expression is a syntactic construct. It must be well-formed : the allowed operators must have the correct number of inputs in the correct places, the characters that make up these inputs must be valid, have a clear order of operationsetc.
Strings of symbols that violate the rules of syntax are not well-formed and are not valid mathematical expressions.
In algebraan expression may be used to designate expresion value, which might depend on values assigned to variables occurring in the expression. The determination of this value depends on mathemstical semantics attached to the symbols of the expression.
The choice of semantics depends on the mathematival of the expression. The how to make a playlist in youtube rules may declare that certain expressions do not designate any value expgession instance when they involve division by 0 ; such expressions are said to have an undefined value, but they are well-formed expressions nonetheless.
In general the meaning of expressions is not limited to exprression values; what does expression mean in mathematical terms instance, an expression might designate a condition, or an equation that is to be solved, or it can be viewed as an object in its own right that can be manipulated according to certain rules.
Formal languages allow formalizing expession concept of well-formed expressions. In the s, a new type of expressions, called lambda expressions how to build a nas, were introduced by Alonzo Church and Stephen Kleene for formalizing functions and their evaluation.
They form the basis for lambda calculusa formal system what conditions can be treated with acupuncture in mathematical logic and the theory of programming languages.
The equivalence of two lambda expressions is undecidable. This is also the case for the expressions representing real numbers, which are built from the integers by using the arithmetical operations, the how to get rid of large facial pores and the exponential Richardson's theorem.
Many mathematical expressions include variables. Any variable can be classified as being either a free variable or a bound variable. For a given combination of values for the free variables, an expression may be evaluated, although for some combinations of values of the free variables, the value of the expression may be undefined.
Thus an expression represents a function whose inputs are the values assigned to the free variables and whose output is the resulting value of the expression. The evaluation of an expression is dependent on the definition of the mathematical operators and on the system of values that is its context. Two expressions are said to be equivalent if, for each combination of values for mathemarical free variables, they have the same output, mathemafical. The expression is equivalent to the simpler expression 12 x.
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Formula that represents a mathematical object. Main article: Syntax. Main articles: Semantics and Formal semantics logic. Main articles: Formal language and Lambda calculus. Algebraic closure Algebraic expression Analytic expression Closed-form expression Combinator Computer matheematical expression Defined and undefined Equation Expression programming Formal grammar Formula Functional wjat Logical expression Term logic.
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Look Up the Meaning of Math Words
Oct 31, · The term of a mathematical expression is separated from other terms with either plus or minus signs and consist of the product a coefficient and one or more variables. A single term may contain an. A mathematical Expression is a combination of symbols that can designate numbers (constants), variables, operations, symbols of grouping and other punctuation. Literal Numerals are letters that stand for numbers (e.g. a, b, x, y). A Constant represents a known value in an algebraic expression. An Expression is a mathematical phrase that combines numbers and/or variables using mathematical operations. An expression is a representation of a value; for example, variables and/or numerals that appear alone or in combination with operators are expressions.
This is a glossary of common mathematical terms used in arithmetic, geometry, algebra, and statistics. Abacus : An early counting tool used for basic arithmetic. Absolute Value : Always a positive number, absolute value refers to the distance of a number from 0.
Addend : A number involved in an addition problem; numbers being added are called addends. Algebra : The branch of mathematics that substitutes letters for numbers to solve for unknown values. Algorithm : A procedure or set of steps used to solve a mathematical computation.
Angle : Two rays sharing the same endpoint called the angle vertex. Angle Bisector : The line dividing an angle into two equal angles. Area : The two-dimensional space taken up by an object or shape, given in square units.
Array : A set of numbers or objects that follow a specific pattern. Attribute : A characteristic or feature of an object—such as size, shape, color, etc.
Average : The average is the same as the mean. Add up a series of numbers and divide the sum by the total number of values to find the average. Base : The bottom of a shape or three-dimensional object, what an object rests on. Base 10 : Number system that assigns place value to numbers.
Bar Graph : A graph that represents data visually using bars of different heights or lengths. Bell Curve : The bell shape created when a line is plotted using data points for an item that meets the criteria of normal distribution.
The center of a bell curve contains the highest value points. Binomial : A polynomial equation with two terms usually joined by a plus or minus sign. Calculus : The branch of mathematics involving derivatives and integrals, Calculus is the study of motion in which changing values are studied.
Capacity : The volume of substance that a container will hold. Centimeter : A metric unit of measurement for length, abbreviated as cm. Circumference : The complete distance around a circle or a square. Chord : A segment joining two points on a circle. Coefficient : A letter or number representing a numerical quantity attached to a term usually at the beginning.
Common Factors : A factor shared by two or more numbers, common factors are numbers that divide exactly into two different numbers. Composite Number : A positive integer with at least one factor aside from its own. Composite numbers cannot be prime because they can be divided exactly. Cone : A three-dimensional shape with only one vertex and a circular base.
Conic Section : The section formed by the intersection of a plane and cone. Constant : A value that does not change. Coordinate : The ordered pair that gives a precise location or position on a coordinate plane.
Congruent : Objects and figures that have the same size and shape. Congruent shapes can be turned into one another with a flip, rotation, or turn. Cosine : In a right triangle, cosine is a ratio that represents the length of a side adjacent to an acute angle to the length of the hypotenuse.
Cylinder : A three-dimensional shape featuring two circle bases connected by a curved tube. Decimal : A real number on the base ten standard numbering system. Denominator : The bottom number of a fraction. The denominator is the total number of equal parts into which the numerator is being divided.
Diagonal : A line segment that connects two vertices in a polygon. Diameter : A line that passes through the center of a circle and divides it in half. Difference : The difference is the answer to a subtraction problem, in which one number is taken away from another.
Digit : Digits are the numerals found in all numbers. Dividend : A number being divided into equal parts inside the bracket in long division. Divisor : A number that divides another number into equal parts outside of the bracket in long division.
Edge : A line is where two faces meet in a three-dimensional structure. Ellipse : An ellipse looks like a slightly flattened circle and is also known as a plane curve. Planetary orbits take the form of ellipses.
End Point : The "point" at which a line or curve ends. Equilateral : A term used to describe a shape whose sides are all of equal length. Equation : A statement that shows the equality of two expressions by joining them with an equals sign.
Even Number : A number that can be divided or is divisible by 2. Event : This term often refers to an outcome of probability; it may answers question about the probability of one scenario happening over another. Evaluate : This word means "to calculate the numerical value".
Exponent : The number that denotes repeated multiplication of a term, shown as a superscript above that term. The exponent of 3 4 is 4. Expressions : Symbols that represent numbers or operations between numbers.
Face : The flat surfaces on a three-dimensional object. Factor : A number that divides into another number exactly. Factoring : The process of breaking numbers down into all of their factors. Factorial Notation : Often used in combinatorics, factorial notations requires that you multiply a number by every number smaller than it.
The symbol used in factorial notation is! When you see x! Factor Tree : A graphical representation showing the factors of a specific number. Fibonacci Sequence : A sequence beginning with a 0 and 1 whereby each number is the sum of the two numbers preceding it. Figure : Two-dimensional shapes. Finite : Not infinite; has an end. Flip : A reflection or mirror image of a two-dimensional shape. Formula : A rule that numerically describes the relationship between two or more variables.
Fraction : A quantity that is not whole that contains a numerator and denominator. Frequency : The number of times an event can happen in a given period of time; often used in probability calculations. Furlong : A unit of measurement representing the side length of one square acre. Geometry : The study of lines, angles, shapes, and their properties. Geometry studies physical shapes and the object dimensions.
Graphing Calculator : A calculator with an advanced screen capable of showing and drawing graphs and other functions. Graph Theory : A branch of mathematics focused on the properties of graphs. Greatest Common Factor : The largest number common to each set of factors that divides both numbers exactly.
The greatest common factor of 10 and 20 is Hexagon : A six-sided and six-angled polygon. Histogram : A graph that uses bars that equal ranges of values. Hyperbola : A type of conic section or symmetrical open curve. The hyperbola is the set of all points in a plane, the difference of whose distance from two fixed points in the plane is a positive constant. Hypotenuse : The longest side of a right-angled triangle, always opposite to the right angle itself. Identity : An equation that is true for variables of any value.
Integers : All whole numbers, positive or negative, including zero. Irrational : A number that cannot be represented as a decimal or fraction. A number like pi is irrational because it contains an infinite number of digits that keep repeating. Many square roots are also irrational numbers. Isosceles : A polygon with two sides of equal length.
Kilometer : A unit of measure equal to meters. Knot : A closed three-dimensional circle that is embedded and cannot be untangled. Like Fractions : Fractions with the same denominator. Line : A straight infinite path joining an infinite number of points in both directions. Line Segment : A straight path that has two endpoints, a beginning and an end.
Linear Equation : An equation that contains two variables and can be plotted on a graph as a straight line. Line of Symmetry : A line that divides a figure into two equal shapes. Logic : Sound reasoning and the formal laws of reasoning. Logarithm : The power to which a base must be raised to produce a given number. Logarithm is the opposite of exponentiation.