Knit shrinkage gauge -- consisting of a set of 20 mounting pins set in guides in radial slots ( Fig. 1 ).

This acquisition is a matched, perfect set -- consisting of two sofas six feet long, plus six sidechairs and two armchairs.

Alternate history or alternative history is a genre of fiction consisting of stories that are set in worlds in which history has diverged from the actual history of the world.

Beowulf (; in Old English or ) is the conventional title of an Old English heroic epic poem consisting of 3182 alliterative long lines, set in Scandinavia, commonly cited as one of the most important works of Anglo-Saxon literature.

One way is simply to list all of its elements ; for example, the set consisting of the integers 3, 4, and 5 may be denoted.

* The cofinality of a partially ordered set with greatest element is 1 as the set consisting only of the greatest element is cofinal ( and must be contained in every other cofinal subset ).

If X is a topological space and M is a complete metric space, then the set C < sub > b </ sub >( X, M ) consisting of all continuous bounded functions ƒ from X to M is a closed subspace of B ( X, M ) and hence also complete.

For each rule with in its RHS, add a set of new rules consisting of the different possible combinations of replaced or not replaced with.

" The Commission recommended legislative remedies consisting of an official Government apology and redress payments of $ 20, 000 to each of the survivors ; a public education fund was set up to help ensure that this would not happen again ( Public Law 100-383 ).

For example, a group is an algebraic object consisting of a set together with a single binary operation, satisfying certain axioms.

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

These are known as Les Grandes Misères de la guerre, consisting of 18 prints published in 1633, and the earlier and incomplete Les Petites Misères – referring to their sizes, large and small ( though even the large set are only about 8 x 13 cm ).

This court ( lagmannsretten ) is administered by a three-judge panel ( usually 1 lagmann and 2 lagdommere ), and if 7 or more jury members want to convict, the sentence is set in a separate proceeding, consisting of the three judges and the jury foreman ( lagrettens ordfører ) and three other members of the jury chosen by ballot.

When the altimeters sensed the correct height, the firing switch closed, igniting the three BuOrd Mk15, Mod 1 Navy gun primers in the breech plug, which set off the charge consisting of four silk powder bags each containing two pounds of WM slotted-tube cordite.

In 1598, a Dutch expedition consisting of eight ships, under the orders of admirals Jacques Cornelius Van Neck and Wybrandt Van Warwyck, set sail from the port of Texel, Netherlands towards the Indian subcontinent.

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.

Prior to the advent of the microprocessor, a computer was usually built in a card-cage case or mainframe with components connected by a backplane consisting of a set of slots themselves connected with wires ; in very old designs the wires were discrete connections between card connector pins, but printed circuit boards soon became the standard practice.

* a " task " is an object consisting of a set of system resources that enable " threads " to run

Experimental studies dating from the 1990s have shown that circadian rhythms are generated by a " genetic clock " consisting of a special set of genes whose expression level rises and falls over the course of the day.

Within 23 minutes of the bombing, the State Emergency Operations Center ( SEOC ) was set up, consisting of representatives from the state departments of public safety, human services, military, health, and education.

This set of enzymes, consisting of complexes I through IV, is called the electron transport chain and is found in the inner membrane of the mitochondrion.

If the negated query can be refuted, i. e., an instantiation for all free variables is found that makes the union of clauses and the singleton set consisting of the negated query false, it follows that the original query, with the found instantiation applied, is a logical consequence of the program.

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

Because of the quantum mechanical nature of the electrons around a nucleus, atomic orbitals can be uniquely defined by a set of integers known as quantum numbers.

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 ."

An example is the " divides " relation between the set of prime numbers P and the set of integers Z, in which every prime p is associated with every integer z that is a multiple of p ( and not with any integer that is not a multiple of p ).

Division of whole numbers can be thought of as a function ; if Z is the set of integers, N < sup >+</ sup > is the set of natural numbers ( except for zero ), and Q is the set of rational numbers, then division is a binary function from Z and N < sup >+</ sup > to Q.

For instance, 4 is a member of the set of all even integers.

: There is no set whose cardinality is strictly between that of the integers and that of the real numbers.

Instead of listing every single element, sometimes an ellipsis ("...") is used, if the writer believes that the reader can easily guess what is missing ; for example, presumably denotes the set of integers from 1 to 100.

What we have done here is arranged the integers and the odd integers into a one-to-one correspondence ( or bijection ), which is a function that maps between two sets such that each element of each set corresponds to a single element in the other set.

For example, Georg Cantor ( who introduced this concept ) demonstrated that the real numbers cannot be put into one-to-one correspondence with the natural numbers ( non-negative integers ), and therefore that the set of real numbers has a greater cardinality than the set of natural numbers.

* Since the p-adic integers are homeomorphic to the Cantor set, they form a compact set.

Given a set of integers, does some nonempty subset of them sum to 0?

An example of an NP-complete problem is the subset sum problem: given a finite set of integers is there a non-empty subset which sums to zero?

The complementary problem is in co-NP and asks: " given a finite set of integers, does every non-empty subset have a nonzero sum?

The concept of being relatively prime can also be extended to any finite set of integers S =

In particular, the circular convolution can be defined for periodic functions ( that is, functions on the circle ), and the discrete convolution can be defined for functions on the set of integers.

* If a set S is in M and S is congruent to T then T is also in M and a ( S )

* " Is congruent to " on the set of all triangles.

* Reduced residue system, a set of φ ( n ) integers such that each integer is relatively prime to n and no two are congruent modulo n

The story is set in the fictional equatorial island country of Taprobane, which Clarke has described as " about ninety percent congruent with the island of Ceylon ( now Sri Lanka )", south of its real world location.

If is the set of tiles in a tessellation, a set of shapes is called a set of prototiles if no two shapes in are congruent to each other, and every tile in is congruent to one of the shapes in.

Given an integer k, one defines the residue class of an integer n as the set of all integers congruent to n modulo k:

Targets were flanked by either a congruent or an incongruent set of letters.

A way of removing the ambiguity of inversion was suggested by Blum and Williams: the two primes used are restricted to primes congruent to 3 modulo 4 and the domain of the squaring is restricted to the set of quadratic residues.

In an attempt to restructure the courses of geometry in Russia, Andrei Kolmogorov suggested presenting it under the point of view of transformations, so the geometry courses were structured based on set theory, this led to the appearance of the term " congruent " in schools, for figures that were before called " equal ": since a figure was seen as a set of points, it could only be equal to itself, and two triangles that could be overlapped by isometries were said to be congruent.

During Seldon's lifetime, congruent points in the Plan were developed and modeled with enough accuracy to determine the critical points of inflexure that would set the Galaxy on the path of Foundation, and the Second Empire.

Also, if two congruent parabolas are set vertex-to-vertex and one is rolled along the other ; the vertex of the rolling parabola will trace the cissoid.

For example, under the group of rigid motions of the plane, the perimeter of a triangle is an invariant, while the set of triangles congruent to a given triangle is a coinvariant.

In classification problems, one seeks to find a complete set of invariants, such that if two objects have the same values for this set of invariants, they are congruent.

For example, triangles such that all three sides are equal are congruent, via SSS congruence, and thus the length of all three sides forms a complete set of invariants for triangles.

" Whereas the word Economy suggests that people in a community possess a common and congruent set of values and goals, Catallaxy suggests that the emergent properties of a market ( prices, division of labor, growth, etc.