In mathematics, a binary relation R on a set X is antisymmetric if, for all a and b in X

Though respected for their contributions to various academic disciplines ( respectively mathematics, linguistics, and literature ), the three men became known to the general public only by making often-controversial and disputed pronouncements on politics and public policy that would not be regarded as noteworthy if offered by a medical doctor or skilled tradesman.

The law embodies the story of a nation's development through many centuries, and it cannot be dealt with as if it contained only the axioms and corollaries of a book of mathematics.

A convex function | function is convex if and only if its Epigraph ( mathematics ) | epigraph, the region ( in green ) above its graph of a function | graph ( in blue ), is a convex set.

In number theory, a branch of mathematics, two integers a and b are said to be coprime ( also spelled co-prime ) or relatively prime if the only positive integer that evenly divides both of them is 1.

In mathematics, the Cauchy – Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which must be satisfied if we know that a complex function is complex differentiable.

In mathematics and the arts, two quantities are in the golden ratio () if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one.

" Although deliberately framed as if it were a law of nature or of mathematics, its purpose has always been rhetorical and pedagogical: I wanted folks who glibly compared someone else to Hitler or to Nazis to think a bit harder about the Holocaust ," Godwin has written.

Isomorphisms are studied in mathematics in order to extend insights from one phenomenon to others: if two objects are isomorphic, then any property that is preserved by an isomorphism and that is true of one of the objects, is also true of the other.

In logic and related fields such as mathematics and philosophy, if and only if ( shortened iff ) is a biconditional logical connective between statements.

He is a seminal figure in the history of mathematics ; if printed, his works, many of which are of fundamental interest, would occupy between 60 and 80 quarto volumes.

In logic and mathematics, a two-place logical operator and, also known as logical conjunction, results in true if both of its operands are true, otherwise the value of false.

In mathematics, however, " or " is always used as inclusive or ; if exclusive or is meant it will be specified, possibly by " xor ".

Such an algorithm contradicts fundamental laws of mathematics because, if it existed, it could be applied repeatedly to losslessly reduce any file to length 0.

Lorentz and Fitzgerald offered within the framework of Lorentz ether theory a more elegant solution to how the motion of an absolute aether could be undetectable ( length contraction ), but if their equations were correct, the new special theory of relativity ( 1905 ) could generate the same mathematics without referring to an aether at all.

In mathematics, the principle that says that if the number of players is one more than the number of chairs, then one player is left standing, is the pigeonhole principle.

* 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

They also objected to students being refused a high school diploma if they could not perform 36 separate mathematics skills, despite being given good grades in class.

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.

Germain decided that if geometry, which at that time referred to all of pure mathematics, could hold such fascination for Archimedes, it was a subject worthy of study.

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 mathematics, a function f is uniformly continuous if, roughly speaking, it is possible to guarantee that f ( x ) and f ( y ) be as close to each other as we please by requiring only that x and y are sufficiently close to each other ; unlike ordinary continuity, the maximum distance between x and y cannot depend on x and y themselves.

In mathematics, the L < sup > p </ sup > spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces.

In mathematics, intuitionism is a program of methodological reform whose motto is that " there are no non-experienced mathematical truths " ( L. E. J.

In July 1739 he made his first contribution to the field of mathematics, pointing out the errors he had detected in L ' analyse démontrée ( published 1708 by Charles René Reynaud ) in a communication addressed to the Académie des Sciences.

At the time L ' analyse démontrée was a standard work, which d ' Alembert himself had used to study the foundations of mathematics.

In mathematics, Minkowski's theorem is the statement that any convex set in R < sup > n </ sup > which is symmetric with respect to the origin and with volume greater than 2 < sup > n </ sup > d ( L ) contains a non-zero lattice point.

It seems that certain mathematicians took this literary challenge literally, and Fadiman follows it with an excerpt from " Ingenious Mathematical Problems and Methods ," by L. A. Graham, who had evidently posed the problem in a mathematics journal.

The mathematics behind the HMM was developed by L. E. Baum and coworkers.

The idea of the Centennial Exposition is credited to John L. Campbell, a professor of mathematics, natural philosophy and astronomy at Wabash College, Crawfordsville, Indiana.

He earned an economics degree from UCLA in 1977 and worked as a high school mathematics teacher in the L. A. public school system for a short period, before pursuing and completing his BFA in 1977.

Intuitionists, such as L. E. J. Brouwer ( 1882 – 1966 ), hold that mathematics is a creation of the human mind.

L. E. J. Brouwer: " On the significance of the principle of excluded middle in mathematics, especially in function theory.

* J. L. Greenberg and J. R. Goodstein, " Theodore von Kármán and applied mathematics in America ," Science 222 ( 4630 ) ( 1983 ), 1300-1304.

* J. L. Greenberg and J. R. Goodstein, " Theodore von Kármán and applied mathematics in America ," A century of mathematics in America II ( Providence, R. I., 1989 ), 467-477.

The University's mathematics centre houses an IBM Blue Gene / L supercomputer for the LOFAR project.

Bernoulli was hired by Guillaume de L ' Hôpital to tutor him in mathematics.

There are two main sub-categories: " Lettres ", in either " A / L " ( with Greek and / or Latin ) or LSH ( with geography ), and B / L ( with mathematics and social sciences ).

In mathematics, the constructible universe ( or Gödel's constructible universe ), denoted L, is a particular class of sets which can be described entirely in terms of simpler sets.

In mathematics, restriction of scalars ( also known as " Weil restriction ") is a functor which, for any finite extension of fields L / k and any algebraic variety X over L, produces another variety Res < sub > L / k </ sub > X, defined over k. It is useful for reducing questions about varieties over large fields to questions about more complicated varieties over smaller fields.

In mathematics, for any Lie algebra L one can construct its universal enveloping algebra U ( L ).