Ordered pairIn mathematics, an ordered pair, denoted (a, b), is a pair of objects in which their order is significant. If a and b are different, then (a,b) is different from (b,a). In contrast, the unordered pair {a,b} always equals the unordered pair {b,a}. Ordered pairs are also called 2-tuples, or sequences (sometimes, lists in a computer science context) of length 2.
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.
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.
Domain of a functionIn mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom(f){\displaystyle \operatorname {dom} (f)} or domf{\displaystyle \operatorname {dom} f}, where f is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be".
Singleton (mathematics)In mathematics, a singleton (also known as a unit set or one-point set) is a set with exactly oneelement. For example, the set {0}{\displaystyle \{0\}} is a singleton whose single element is 0{\displaystyle 0}. PropertiesWithin the framework of Zermelo–Fraenkel set theory, the axiom of regularity guarantees that no set is an element of itself.
Recurrence relationIn mathematics and computer science, a recurrence relation is an equation according to which the n{\displaystyle n}th term of a sequence of numbers is equal to some combination of the previous terms. Often, only k{\displaystyle k} previous terms of the sequence appear in the equation, for a parameter k{\displaystyle k} that is independent of n{\displaystyle n}; this number k{\displaystyle k} is called the order of the relation.
Natural numberNatural numbers can be used for counting: one apple plus two apples equals three apples.In mathematics, the natural numbers are the numbers used for counting up, starting from 0 or 1. The first few natural numbers are 0 (if included), 1, 2, 3, and so on. The terms positive integers, non-negative integers, whole numbers, and counting numbers are also used. The set of the natural numbers is commonly denoted by a bold N or a blackboard boldN{\displaystyle \mathbb {N} }.
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.
Image (mathematics)In mathematics, the image of a functionf:X→Y{\displaystyle f:X\to Y} is the set of all f(x){\displaystyle f(x)} such that x{\displaystyle x} belongs to the domain of f{\displaystyle f}. The image by f{\displaystyle f} of an element x{\displaystyle x} of the domain of f{\displaystyle f} is f(x){\displaystyle f(x)}, that is, the output corresponding to the input x{\displaystyle x}.
IntegerAn integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.
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.
Mathematical objectA mathematical object is an abstract entity 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.
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