* Absorption law, in mathematics, an identity linking a pair of binary operations

In mathematics, an identity function, also called identity map or identity transformation, is a function that always returns the same value that was used as its argument.

In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.

* Neutral element or identity element ( mathematics ), a special type of element of a set with respect to a binary operation on that set, such if applied to, or operated with any element of the set, causes no change to this last element

In mathematics, de Moivre's formula ( a. k. a. De Moivre's theorem and De Moivre's identity ), named after Abraham de Moivre, states that for any complex number ( and, in particular, for any real number ) x and integer n it holds that

According to general semantics, the content of all knowledge is structure, so that language ( in general ) and science and mathematics ( in particular ) can provide people with a structural ' map ' of empirical facts, but there can be no ' identity ', only structural similarity, between the language ( map ) and the empirical facts as lived through and observed by people as humans-in-environments ( including doctrinal and linguistic environments ).

More mundanely, an identity in mathematics may be an equation that holds true for all values of a variable.

In mathematics, Itō's lemma is an identity used in Itō calculus to find the differential of a time-dependent function of a stochastic process ; it serves as the stochastic calculus counterpart of the chain rule.

In mathematics, Euler's four-square identity says that the product of two numbers, each of which is a sum of four squares, is itself a sum of four squares.

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1 / x or x < sup >− 1 </ sup >, is a number which when multiplied by x yields the multiplicative identity, 1.

In mathematics the Jacobi identity is a property that a binary operation can satisfy which determines how the order of evaluation behaves for the given operation.

In mathematics, the term identity has several different important meanings:

Gerdes ' writings about how mathematics can be used in the school systems of Mozambique and South Africa, and D ' Ambrosio's 1990 discussion of the role mathematics plays in building a democratic and just society are examples of the impact mathematics can have on developing the identity of a society.

In mathematics, the simplest form of the parallelogram law ( also called the parallelogram identity ) belongs to elementary geometry.

Faà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives, named after, though he was not the first to state or prove the formula.

In mathematics, the cyclotomic identity states that

In mathematics ( specifically linear algebra ), the Woodbury matrix identity, named after Max A. Woodbury says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix.

In mathematics, a unital algebra or unitary algebra is an algebra which contains a multiplicative identity element ( or unit ), i. e. an element 1 with the property 1x

In mathematics, a semigroupoid is a partial algebra which satisfies the axioms for a small category, except possibly for the requirement that there be an identity at each object.

In mathematics, complex multiplication is the theory of elliptic curves E that have an endomorphism ring larger than the integers ; and also the theory in higher dimensions of abelian varieties A having enough endomorphisms in a certain precise sense ( it roughly means that the action on the tangent space at the identity element of A is a direct sum of one-dimensional modules ).

* Absorbing element, in mathematics, an element that does not change when it is combined in a binary operation with some other element

In mathematics, a binary operation on a set is a calculation involving two elements of the set ( called operands ) and producing another element of the set ( more formally, an operation whose arity is two ).

In mathematics, a bilinear operator is a function combining elements of two vector spaces to yield an element of a third vector space that is linear in each of its arguments.

" In addition, the element Earth is associated with Budha or Mercury who represents communication, business, mathematics and other practical matters.

In mathematics, an equivalence relation is a relation that, loosely speaking, partitions a set so that every element of the set is a member of one and only one cell of the partition.

In mathematics, given a set and an equivalence relation on, the equivalence class of an element in is the subset of all elements in which are equivalent to.

In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element.

In mathematics, given a prime number p, a p-group is a periodic group in which each element has a power of p as its order: each element is of prime power order.

In mathematics a topological space is called separable if it contains a countable dense subset ; that is, there exists a sequence of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.

In mathematics, a function f from a set X to a set Y is surjective ( or onto ), or a surjection, if every element y in Y has a corresponding element x in X so that f ( x ) = y.

In pure mathematics, a vector is defined more generally as any element of a vector space.

In pure mathematics, a vector is any element of a vector space over some field and is often represented as a coordinate vector.

This is an unsolved problem which probably has never been seriously investigated, although one frequently hears the comment that we have insufficient specialists of the kind who can compete with the Germans or Swiss, for example, in precision machinery and mathematics, or the Finns in geochemistry.

Next September, after receiving a degree from Yale's Master of Arts in Teaching Program, I will be teaching somewhere -- that much is guaranteed by the present shortage of mathematics teachers.

But because science is based on mathematics doesn't mean that a hot rodder must necessarily be a mathematician.

Like primitive numbers in mathematics, the entire axiological framework is taken to rest upon its operational worth.

In the new situation, philosophy is able to provide the social sciences with the same guidance that mathematics offers the physical sciences, a reservoir of logical relations that can be used in framing hypotheses having explanatory and predictive value.

So, too, is the mathematical competence of a college graduate who has majored in mathematics.

The principal of the school announced that -- despite the help of private tutors in Hollywood and Philadelphia -- Fabian is a 10-o'clock scholar in English and mathematics.

In mathematics and statistics, the arithmetic mean, or simply the mean or average when the context is clear, is the central tendency of a collection of numbers taken as the sum of the numbers divided by the size of the collection.

The term " arithmetic mean " is preferred in mathematics and statistics because it helps distinguish it from other means such as the geometric and harmonic mean.

In addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, though it is used in almost every academic field to some extent.

The use of the soroban is still taught in Japanese primary schools as part of mathematics, primarily as an aid to faster mental calculation.

In mathematics and computer science, an algorithm ( originating from al-Khwārizmī, the famous Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī ) is a step-by-step procedure for calculations.

In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that " the product of a collection of non-empty sets is non-empty ".

The axiom of choice is avoided in some varieties of constructive mathematics, although there are varieties of constructive mathematics in which the axiom of choice is embraced.

The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where non-classical logic is employed.

:" A choice function exists in constructive mathematics, because a choice is implied by the very meaning of existence.

Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.

One of the most interesting aspects of the axiom of choice is the large number of places in mathematics that it shows up.

There is no prize awarded for mathematics, but see Abel Prize.