SequenceIn mathematics, a sequence is a collection of objects possibly with repetition, that come in a specified order. Like a set, it contains members (also called elements, or terms). Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. The notion of a sequence can be generalized to an indexed family, defined as a function from an arbitrary index set.
AdditionAddition, usually denoted with the plus sign +, is one of the four basic operations of arithmetic, the other three being subtraction, multiplication, and division. The addition of two whole numbers results in the total or sum of those values combined. For example, the adjacent image shows two columns of apples, one with three apples and the other with two apples, totaling to five apples.
PolynomialType of mathematical expressionIn mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of a single indeterminate x{\displaystyle x} is x2−4x+7{\displaystyle x^{2}-4x+7}.
Series (mathematics)Infinite sum Integral Series Vector Multivariable Advanced Specialized Fractional Malliavin Stochastic Variations Miscellanea Precalculus History Glossary List of topics Integration Bee Mathematical analysis Nonstandard analysis vte In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other. The study of series is a major part of calculus and its generalization, mathematical analysis.
Vector spaceAlgebraic structure in linear algebraVector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2w.In mathematics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars.
Function (mathematics)Association of one output to each inputIn mathematics, a function from a setX to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time.
MathematicsMathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems in science, engineering, technology, economics, and everyday life.
Operation (mathematics)In mathematics, an operation is a function that takes as input a fixed number of elements of a set and returns an element of the same set. For example, addition on real numbers is an operation that accepts two real numbers and returns a real number. In general, the input values may be called "operands" or "arguments". The number of operands is the arity of the operation. The arity is usually one of 0,1,2,…{\displaystyle 0,1,2,\ldots }.
NumberUsed to count, measure, and labelSet inclusions between the natural numbers (ℕ), the integers (ℤ), the decimal fractions (𝔻), the rational numbers (ℚ), the real numbers (ℝ), and the complex numbers (ℂ)A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers: 1, 2, 3, 4, 5, and so forth.
Matrix (mathematics)Array of numbersAn m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts.
Mathematical objectA mathematical object is an abstract concept arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a symbol, and therefore can be involved in formulas. Commonly encountered mathematical objects include numbers, expressions, shapes, functions, and sets. Mathematical objects can be very complex; for example, theorems, proofs, and even formal theories are considered as mathematical objects in proof theory.*As an Amazon Associate I earn from qualifying purchases.