In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum ( join ) and an infimum ( meet ).

In mathematics, the limit inferior ( also called infimum limit, liminf, inferior limit, lower limit, or inner limit ) and limit superior ( also called supremum limit, limsup, superior limit, upper limit, or outer limit ) of a sequence can be thought of as limiting ( i. e., eventual and extreme ) bounds on the sequence.

In mathematics, a lattice is a partially ordered set in which any two elements have a supremum ( also called a least upper bound or join ) and an infimum ( also called a greatest lower bound or meet ).

" The word " mathematics " may have originally been plural in concept, referring to mathematic endeavors, but metonymic shift — that is, the shift in concept from " the endeavors " to " the whole set of endeavors "— produced the usage of " mathematics " as a singular entity taking singular verb forms.

In mathematics, a lemma ( plural lemmata or lemmas ) from the Greek λῆμμα ( lemma, “ anything which is received, such as a gift, profit, or a bribe ”) is a proven proposition which is used as a stepping stone to a larger result rather than as a statement of interest by itself.

In mathematics, a parabola (; plural parabolae or parabolas, from the Greek παραβολή ) is a conic section, created from the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface.

The applied tools of the mathematics disciplines of Celestial mechanics or its subfield Orbital mechanics ( both predict orbital paths and positions ) about a center of gravity are used to generate an ephemeris ( plural: ephemerides ; from the Greek word ephemeros = daily ) which is a table of values that gives the positions of astronomical objects in the sky at a given time or times, or a formula to calculate such given the proper time offset from the epoch.

As with English, most uncountable nouns are grammatically treated as singular, though some are plural, such as les mathématiques (" mathematics "), and some nouns that are uncountable in English are countable in French, such as une information (" a piece of information "), or une nouvelle (" a piece of news, a news item ").

In mathematics, abscissa ( plural abscissae or abscissæ ) refers to that element of an ordered pair which is plotted on the horizontal axis of a two-dimensional Cartesian coordinate system, as opposed to the ordinate.

In mathematics, genus ( plural genera ) has a few different, but closely related, meanings:

In mathematics, the maximum and minimum ( plural: maxima and minima ) of a function, known collectively as extrema ( singular: extremum ), are the largest and smallest value that the function takes at a point either within a given neighborhood ( local or relative extremum ) or on the function domain in its entirety ( global or absolute extremum ).

In mathematics, an annulus ( the Latin word for " little ring ", with plural annuli ) is a ring-shaped geometric figure, or more generally, a term used to name a ring-shaped object.

In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular values.

Several writers have suggested that plural logic opens the prospect of simplifying the foundations of mathematics, avoiding the paradoxes of set theory, and " simplifying the complex and unintuitive axiom sets needed in order to avoid them.

Other words originally plural have been notionally singular for so long that it is always considered correct to follow them by a singular verb: news, means, and mathematics.

In mathematics, a dessin d ' enfant ( French for a " child's drawing ", plural dessins d ' enfants, " children's drawings ") is a type of graph drawing used to study Riemann surfaces and to provide combinatorial invariants for the action of the absolute Galois group of the rational numbers.

In mathematics, a countable set is a set with the same cardinality ( number of elements ) as some subset of the set of natural numbers.

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 certain kind of subset of a partially ordered set.

** Filter ( mathematics ), a special subset of a partially ordered set

* Interval ( mathematics ), a range of numbers ( formally, a type of subset of an ordered set )

In mathematics, a filter is a special subset of a partially ordered set.

In algebra ( which is a branch of mathematics ), a prime ideal is a subset of a ring which shares many important properties of a prime number in the ring of integers.

In mathematics, especially in set theory, a set A is a subset of a set B, or equivalently B is a superset of A, if A is " contained " inside B, that is, all elements of A are also elements of B.

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 well-order relation ( or well-ordering ) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering.

* Core ( functional analysis ), in mathematics, a subset of the domain of a closable operator

In mathematics, the closure of a subset S in a topological space consists of all points in S plus the limit points of S. Intuitively, these are all the points that are " near " S. A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to the notion of interior.

In mathematics, given a subset S of a totally or partially ordered set T, the supremum ( sup ) of S, if it exists, is the least element of T that is greater than or equal to every element of S. Consequently, the supremum is also referred to as the least upper bound ( lub or LUB ).

In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set ( P, ≤) is an element of P which is greater than or equal to every element of S. The term lower bound is defined dually as an element of P which is less than or equal to every element of S. A set with an upper bound is said to be bounded from above by that bound, a set with a lower bound is said to be bounded from below by that bound.

In mathematics, a complete measure ( or, more precisely, a complete measure space ) is a measure space in which every subset of every null set is measurable ( having measure zero ).

In mathematics, subalgebra is a subset of an algebra, closed under all its operations, and carrying the induced operations.

* Closure ( mathematics ), the smallest object that both includes the object as a subset and possesses some given property

The notions of a " decidable subset " and " recursively enumerable subset " are basic ones for classical mathematics and classical logic.

In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom schema of specification, axiom schema of separation, subset axiom scheme or axiom schema of restricted comprehension, is a schema of axioms in Zermelo – Fraenkel set theory.

In topology and related fields of mathematics, a topological space X is called a regular space if every non-empty closed subset C of X and a point p not contained in C admit non-overlapping open neighborhoods.

In mathematics, logic and computer science, a formal language is called recursively enumerable ( also recognizable, partially decidable or Turing-acceptable ) if it is a recursively enumerable subset in the set of all possible words over the alphabet of the language, i. e., if there exists a Turing machine which will enumerate all valid strings of the language.

In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f: U → R ( where U is an open subset of R < sup > n </ sup >) which satisfies Laplace's equation, i. e.

Reacting against authors such as J. S. Mill, Sigwart and his own former teacher Brentano, Husserl criticised their psychologism in mathematics and logic, i. e. their conception of these abstract and a-priori sciences as having an essentially empirical foundation and a prescriptive or descriptive nature.

In mathematics, Horner's method ( also known as Horner scheme in the UK or Horner's rule in the U. S .) is either of two things: ( i ) an algorithm for calculating polynomials, which consists in transforming the monomial form into a computationally efficient form ; or ( ii ) a method for approximating the roots of a polynomial.

He started studying mathematics in 1941 in the U. S., but his studies were interrupted by the war, during which he served in the military.

Quite unhappy with the lack of formal science education at Eton College, Maynard Smith took it upon himself to develop an interest in Darwinian evolutionary theory and mathematics, after having read the work of old Etonian J. B. S.

* A. S. Troelstra ( 1977a ), " Aspects of constructive mathematics ", Handbook of Mathematical Logic, pp. 973 – 1052.

Enrollment in computer-related degrees in U. S. has dropped recently due to lack of general interests in science and mathematics and also out of an apparent fear that programming will be subject to the same pressures as manufacturing and agriculture careers.

* Phillip S. Jones, Jack D. Bedient: The historical roots of elementary mathematics.

In mathematics, the symmetric group S < sub > n </ sub > on a finite set of n symbols is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself.

Such exploits made Knuth a topic of discussion among the mathematics department, which included Richard S. Varga.