With each vertex we associate certain numerical values, namely the set of positive differences in the parameter T between the vertex and its corresponding forward corner points.

We first define a function b{t} as follows: given the set of squares such that each has three corners on C and vertex at t, b{t} is the corresponding set of positive parametric differences between T and the backward corner points.

In number theory, an arithmetic, arithmetical, or number-theoretic function is a real or complex valued function ƒ ( n ) defined on the set of natural numbers ( i. e. positive integers ) that " expresses some arithmetical property of n ."

The symbol μ denotes a positive measure: that is, a real-valued positive set function defined on a σ-algebra which is countably additive.

I regret that .... I wish I had gotten up then and seized the moment to set a tone, a tone that I had set in Texas, a positive and inclusive tone.

Even more important: a difference generally implies positive terms between which the difference is set up ; but in language there are only differences without positive terms.

The ellipse can also be defined as the set of points such that the distance from any point in that set to a given point in the plane ( a focus ) is a constant positive fraction less than 1 ( the eccentricity ) of the perpendicular distance of the point in the set to a given line ( called the directrix ).

For any positive integer n, the set of all n-tuples of real numbers forms an n-dimensional vector space over R, which is denoted R < sup > n </ sup > and sometimes called real coordinate space.

For example, the set of all positive integers is infinite:

Insurers set their premiums to obtain a long term positive expected return in the same manner that professional gamblers select which bets to make.

For example, operation-preserving functions exist between the set of real numbers with addition and the set of positive real numbers with multiplication.

" Nonstate theorists rejected the idea of hypnotic trance and interpret the effects of hypnotism as due to a combination of multiple task-specific factors derived from normal cognitive, behavioural, and social psychology, such as social role-perception and favorable motivation ( Sarbin ), active imagination and positive cognitive set ( Barber ), response expectancy ( Kirsch ), and the active use of task-specific subjective strategies ( Spanos ).

In particular, Barber argued that responses to hypnotic suggestions were mediated by a " positive cognitive set " consisting of positive expectations, attitudes, and motivation.

Furthermore, as noted by Bohr, Moseley's law provided a reasonably complete experimental set of data that supported the ( new from 1911 ) conception by Ernest Rutherford and Antonius Van den Broek of the atom, with a positively-charged nucleus surrounded by negatively-charged electrons in which the atomic number is understood to be the exact physical number of positive charges ( later discovered and called protons ) in the central atomic nuclei of the elements.

It is defined for a set of n positive numbers x < sub > i </ sub > by

by a finite set of positive operators

There is no universal agreement about whether to include zero in the set of natural numbers: some define the natural numbers to be the positive integers

And the best way to conceal and disguise the elements of an incest story is not to set out to write an incest story.

A set of tables containing spectral intensities for 39,000 lines of 70 elements, as observed in a copper matrix in a d-c arc, was completed and published.

This is not the most general situation of a Cartesian product of a family of sets, where a same set can occur more than once as a factor ; however, one can focus on elements of such a product that select the same element every time a given set appears as factor, and such elements correspond to an element of the Cartesian product of all distinct sets in the family.

The difficulty appears when there is no natural choice of elements from each set.

* In set theory, an automorphism of a set X is an arbitrary permutation of the elements of X.

Similarly, the subset order ⊆ on the subsets of any given set is antisymmetric: given two sets A and B, if every element in A also is in B and every element in B is also in A, then A and B must contain all the same elements and therefore be equal:

The repeating periodicity of the blocks of 2, 6, 10, and 14 elements within sections of the periodic table arises naturally from the total number of electrons which occupy a complete set of s, p, d and f atomic orbitals, respectively.

Another set of methods is the aromatization of cyclohexanes and other aliphatic rings: reagents are catalysts used in hydrogenation such as platinum, palladium and nickel ( reverse hydrogenation ), quinones and the elements sulfur and selenium.

* Consider a set with three elements, A, B, and C. The following operation:

The set of valid index tuples and the addresses of the elements ( and hence the element addressing formula ) are usually, but not always, fixed while the array is in use.

In addition to omitting the axiom of regularity, non-standard set theories have indeed postulated the existence of sets that are elements of themselves.

An abelian group is a set, A, together with an operation "•" that combines any two elements a and b to form another element denoted.

The set of all invertible elements is therefore closed under multiplication and forms a Moufang loop.

A partially ordered set ( poset ) P is said to satisfy the ascending chain condition ( ACC ) if every ascending chain of elements eventually terminates.

In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A.

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 ).

More precisely, a binary operation on a non-empty set S is a map which sends elements of the Cartesian product S × S to S:

* Base ( group theory ), a sequence of distinct elements of a set

Bartók and Kodály quickly set about incorporating elements of such Magyar peasant music into their compositions.

He held that no group of colonists could set up or maintain a government without royal sanction.

Compound comparisons typically compare two sets of groups means where one set has two or more groups ( e. g., compare average group means of group A, B and C with group D ).

** For every non-empty set S there is a binary operation defined on S that makes it a group.

The set of all automorphisms of an object forms a group, called the automorphism group.

If the automorphisms of an object X form a set ( instead of a proper class ), then they form a group under composition of morphisms.

* In elementary arithmetic, the set of integers, Z, considered as a group under addition, has a unique nontrivial automorphism: negation.

He says in the page 114 of his autobiography that he was responsible for the null set symbol ( Ø ) and it came from the Norwegian alphabet, with which he alone among the Bourbaki group was familiar.

The Ann Arbor Land Company, a group of speculators, set aside of undeveloped land and offered it to the state of Michigan as the site of the state capital, but lost the bid to Lansing.

Shortly thereafter, they set off with a small group of followers for Europe.

To qualify as an abelian group, the set and operation,, must satisfy five requirements known as the abelian group axioms:

* Generating set of a group

* Bicycle User Group, a group set up to promote cycling issues

The set of invertible elements in any unital Banach algebra is an open set, and the inversion operation on this set is continuous, ( and hence homeomorphism ) so that it forms a topological group under multiplication.

A set of house rules may be accepted as valid by a group of players wherever they play, as it may also be accepted as governing all play within a particular house, café, or club.

Since over the course of any single dance, individuals interact with not just their partners but everyone else in the set, contra dancing might be considered a group activity.

The earliest and most famous example is Code of Hammurabi which set the different punishment and compensation according to the different class / group of victims and perpetrators.

The show is set in the Cheers bar ( named for the toast " Cheers ") in Boston, Massachusetts, where a group of locals meet to drink, relax, chat and have fun.