Their expressed standards concerning sex roles, desirable age for marriage, characteristics of an ideal mate, number of children desired are congruent with the values and stereotypes of the preceding generation -- minus compulsive rebellion.

In other words, the circle gets partitioned into a countable collection of disjoint sets, which are all pairwise congruent.

Although they take their names from the mentioned historic provinces, the dialect boundaries are not congruent with province boundaries.

Binary relations are used in many branches of mathematics to model concepts like " is greater than ", " is equal to ", and " divides " in arithmetic, " is congruent to " in geometry, " is adjacent to " in graph theory, " is orthogonal to " in linear algebra and many more.

Furthermore, all solutions x of this system are congruent modulo the product, N = n < sub > 1 </ sub > n < sub > 2 </ sub >… n < sub > k </ sub >.

All solutions x are then congruent modulo the least common multiple of the n < sub > i </ sub >.

For example, every polygon is topologically self-dual ( it has the same number of vertices as edges, and these are switched by duality ), but will not in general be geometrically self-dual ( up to rigid motion, for instance ) – regular polygons are geometrically self-dual ( all angles are congruent, as are all edges, so under duality these congruences swap ), but irregular polygons may not be geometrically self-dual.

The two figures on the left are congruent, while the third is Similarity ( geometry ) | similar to them.

Alternatively, two figures are congruent if one can be moved on top of the other so that it matches up with it exactly.

) Thus, for example, a 2x6 rectangle and a 3x4 rectangle are equal but not congruent, and the letter R is congruent to its mirror image.

Figures that would be congruent except for their differing sizes are referred to as similar.

Triangles are congruent if they have all three sides equal ( SSS ), two sides and the angle between them equal ( SAS ), or two angles and a side equal ( ASA ) ( Book I, propositions 4, 8, and 26 ).

( Triangles with three equal angles are generally similar, but not necessarily congruent.

Also, triangles with two equal sides and an adjacent angle are not necessarily equal or congruent.

Jews have interacted with Muslims since the 7th century, when Islam originated and spread in the Arabian peninsula, and many aspects of Islam's core values, structure, jurisprudence and practice are congruent with Judaism.

It is also not known whether infinitely many Mersenne numbers with prime exponents are composite, although this would follow from widely believed conjectures about prime numbers, for example, the infinitude of Sophie Germain primes congruent to 3 ( mod 4 ).

For a positive integer n, two integers a and b are said to be congruent modulo n, written:

Line QP can be extended beyond P to some point T, and line GP can be extended beyond P to some point R. Then and are vertical, so they are equal ( congruent ).

The faces are congruent, regular polygons, with the same number of faces meeting at each vertex.

* Prisms, where the polygons in each plane are congruent and joined by rectangles or parallelograms ;

The outputs are added modulo 2 < sup > 32 </ sup > and XORed to produce the final 32-bit output.

* Every pair of congruence relations for an unknown integer x, of the form x ≡ k ( mod a ) and x ≡ l ( mod b ), has a solution, as stated by the Chinese remainder theorem ; in fact the solutions are described by a single congruence relation modulo ab.

As a consequence of the third point, if a and b are coprime and br ≡ bs ( mod a ), then r ≡ s ( mod a ) ( because we may " divide by b " when working modulo a ).

Furthermore, if b < sub > 1 </ sub > and b < sub > 2 </ sub > are both coprime with a, then so is their product b < sub > 1 </ sub > b < sub > 2 </ sub > ( modulo a it is a product of invertible elements, and therefore invertible ); this also follows from the first point by Euclid's lemma, which states that if a prime number p divides a product bc, then p divides at least one of the factors b, c.

A wide range of identities are used that are true modulo certain subgroups.

( As usual, the subscripts are interpreted modulo N ; thus, for, we have.

Here ( Z / 2Z ) is the polynomial ring of Z / 2Z and ( Z / 2Z )/( T < sup > 2 </ sup >+ T + 1 ) are the equivalence classes of these polynomials modulo T < sup > 2 </ sup >+ T + 1.

Lifting is most important when, the Jacobson radical of R. Yet another characterization of semiperfect rings is that they are semilocal rings whose idempotents lift modulo J ( R ).

Other common kinds of polynomials are polynomials with integer coefficients, polynomials with complex coefficients, and polynomials with coefficients that are integers modulo of some prime number p. In most of the examples in this section, the coefficients are integers.

* 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 output byte is selected by looking up the values of S ( i ) and S ( j ), adding them together modulo 256, and then looking up the sum in S ; S ( S ( i ) + S ( j )) is used as a byte of the key stream, K. For as many iterations as are needed, the PRGA modifies the state and outputs a byte of the keystream.

Another typical example is the statement that " there are two different groups of order 4 up to isomorphism ", or " modulo isomorphism, there are two groups of order 4 ".

For a given positive integer, two integers and are called congruent modulo, written

for example, and are congruent modulo,

( There are different definitions for the modulo operation.

The positive integer Gaussian primes are the prime numbers congruent to 3 modulo 4,.

* For compatibility: Messages are typically bit strings, but some signature schemes operate on other domains ( such as, in the case of RSA, numbers modulo a composite number N ).

The angles that are constructible form an abelian group under addition modulo 2π ( which corresponds to multiplication of the points on the unit circle viewed as complex numbers ).

this is not so, for education offers all kinds of dividends, including how to pull the wool over a husband's eyes while you are having an affair with his wife.

and I have heard many say that they are content to earn a half or a third as much as they could up North because they so much prefer the quieter habits of their home town.

Accidental war is so sensitive a subject that most of the people who could become directly involved in one are told just enough so they can perform their portions of incredibly complex tasks.

They are huge areas which have been swept by winds for so many centuries that there is no soil left, but only deep bare ridges fifty or sixty yards apart with ravines between them thirty or forty feet deep and the only thing that moves is a scuttling layer of sand.

Lucretius has remarked: `` The reason why all Mortals are so gripped by fear is that they see all sorts of things happening in the earth and sky with no discernable cause, and these they attribute to the will of God ''.

In fact, insofar as science generates any fear, it stems not so much from scientific prowess and gadgets but from the fact that new unanswered questions arise, which, until they are understood, create uncertainty.

That is why, the argument runs, the squares are so fearful of jazz and yet perversely fascinated by it.

The party is usually in a room small enough so that all guests are within sight and hearing of one another.

Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

The assumptions upon which the example shown in Figure 3 is based are: ( A ) One man can direct about six subordinates if the subordinates are chosen carefully so that they do not need too much personal coaching, indoctrinating, etc..

These assumptions lead to an organization with one man at the top, six directly under him, six under each of these, and so on until there are six levels of personnel.

Not discussed here are some military problems of modern times such as undersea warfare, where the surveillance, sending, transmitting, and receiving are all so inadequate that networks and decision making are not the bottlenecks.

Such problems are of extreme interest as well as importance and are so much like fighting in a rain forest or guerrilla warfare at night in tall grass that we might have to re-examine primitive conflicts for what they could teach.

We have so completely entered the child's fantasy that his illness and his death are the plausible and the necessary conclusion.

What is more, the legends have become so sacrosanct that the very habit of self-examination or self-criticism smells of low treason, and men who practice it are defeatists and unpatriotic scoundrels.

The Axioms required to make the theoretical machinery operate are set out tersely and powerfully, so that all permissible operations within the theory can be traced rigorously back to these axioms, rules, and primitive notions.

One is so accustomed to think of men as the privileged who need but ask and receive, and women as submissive and yielding, that our sympathies are usually enlisted on the side of the man whose love is not returned, and we condemn the woman as a coquette.

Here, in two nations alone, are almost five hundred million people, all working, and working hard, to raise their standards, and in doing so, to make of themselves a strong bulwark against the spread of an ideology that would destroy liberty.

Second, our military missile program, going forward so successfully, does not suffer from our present lack of very large rocket engines, which are necessary in distant space exploration.

The reasons for the Whig joy on this occasion are found to be their expectation of regaining control of the government, their delight at the prospect of a new war, their hopes of having the Tories hanged, and so on.