`` Tact '', by its very derivation, implies that its possessor keeps in touch with other people, but the author of Clericis Laicos and Unam Sanctam, the wielder of the two swords, the papal sun of which the imperial moon was but a dim reflection, the peer of Caesar and vice-regent of Christ, was so high above other human beings that he had forgotten what they were like.

Scholars have often believed that Ammianus ' work was intended for public recitation for two reasons: the overwhelming presence of accentual clausulae, which implies that it was intended to be read aloud ; and epistle 1063 of Libanius to a Marcellinus of Rome which refers to public recitations.

# Herodotus nowhere states or implies that peace was concluded between the two states before 481 BC, nor does he distinguish between different wars during this period.

In byte-oriented systems ( i. e. most modern computers ), the term uncompressed BCD usually implies a full byte for each digit ( often including a sign ), whereas packed BCD typically encodes two decimal digits within a single byte by taking advantage of the fact that four bits are enough to represent the range 0 to 9.

All of the earliest chordate fossils have been found in the Early Cambrian Chengjiang fauna, and include two species that are regarded as fish, which implies they are vertebrates.

The word video in video game traditionally referred to a cathode ray tube ( CRT ) display device, but it now implies any type of display device that can produce two or three dimensional images.

The sculpture implies two types of cavalry, but this might be a simplification by the artist.

Although ditheism / bitheism imply moral dualism, they are not equivalent: ditheism / bitheism implies ( at least ) two gods, while moral dualism does not imply any-theism ( theos = god ) whatsoever.

If ~ and ≈ are two equivalence relations on the same set S, and a ~ b implies a ≈ b for all a, b ∈ S, then ≈ is said to be a coarser relation than ~, and ~ is a finer relation than ≈.

For if k, m, and n are integers, and k is a common factor of two integers A and B, then A = nk and B = mk implies A − B = ( n − m ) k, therefore k is also a common factor of the difference.

As their name implies, four-stroke internal combustion engines have four basic steps that repeat with every two revolutions of the engine:

Equality is when two objects are exactly the same, and everything that's true about one object is true about the other, while an isomorphism implies everything that's true about a designated part of one object's structure is true about the other's.

This equation implies two things.

Proportionality, by definition, implies that two values have a constant ratio:

The impossibility of flattening the sphere to the plane implies that no map projection can have constant scale: on most projections the best we can achieve is accurate scale on one or two lines ( not necessarily straight ) on the projection.

This implies an increased signal-to-noise ratio in the circuits connecting the two regions.

The term " nation state " implies that the two geographically coincide.

As for the objection [...] that the distance between two distinct real numbers cannot be infinitely small, G. W. Leibniz argued that the theory of infinitesimals implies the introduction of ideal numbers which might be infinitely small or infinitely large compared with the real numbers but which were to possess the same properties as the latter.

The relatively recent name of " Muscat and Oman " ( which was abolished in 1970 in favor of " Sultanate of Oman "), implies two historically irreconcilable political cultures: the coastal tradition, the more cosmopolitan, secular, Muscat tradition of the coast ruled by the sultan ; and the interior tradition of insularity, tribal in origin and ruled by an imam according to the ideological tenets of Ibadism.

For instance, The Visitation implies the importance of collaboration of black communities by depicting intimacy between two black women who are holding hands together.

We make two observations: ( a ) is a linear combination of vectors in the row space of, which implies that belongs to the row space of, and ( b ) since = 0, is orthogonal to every row vector of and, hence, is orthogonal to every vector in the row space of.

In addition, the skeptics argued that two propositions could not rely on each other, as this would create a circular argument ( as p implies q and q implies p ).

Leibniz argued that space could not exist independently of objects in the world because that implies a difference between two universes exactly alike except for the location of the material world in each universe.

As a result there are many misconceptions to what the term specifically implies.

If internal responsibility suggests acceptance of the socialist ideal of equality, then external responsibility implies adherence to principles of ideological supranationalism.

Faulkner's is not the mind of the apologist which Mr. O'Donnell implies that it is.

That implies that Shann was on the enemy side.

Such, he implies, is the case with his friend, who is not really a new convert himself but merely a favorer of new converts.

This, no doubt, is part of what Gilbert Seldes implies when he says of the arts, `` They give form and meaning to life which might otherwise seem shapeless and without sense ''.

Forgiveness implies more than a person wanting his past sins covered by God's love.

It also implies that a man wants his future to be free from the mistakes of the past.

A randomization of `` ups '' and `` downs '' is more likely than ordered `` ups '' and `` downs '' in position ( 3 ) since the hydrogen atoms are well separated and so the position of one could hardly affect the position of another, and also since ordered `` up '' and `` down '' implies a larger unit cell, for which no evidence exists.

Since C is rational, this correspondence has K coincidences, each of which implies a line of the pencil which meets its image.

In I knew you when you were a child, and you were pretty then dominant stress on then implies that the young woman spoken to is still pretty.

The very idea of there being `` count rules '' implies that there is some sort of proportion to be expected between the amount of congestive activity and the extent of the breakaway ( run up or run down ) movement.

In contrast to this Stoic-patristic view, Utopia implies that the nature of man is such that to rely on individual conscience to supply the deficiencies of municipal law is to embark on the bottomless sea of human sinfulness in a sieve.

The respectability which money confers implies a different etiquette, and, upon taking up the life of a London gentleman, Pip must learn from Herbert Pocket that `` the spoon is not generally used over-hand, but under ''.

The general tone of articles appearing in such important newspapers as the Manchester Guardian and the Sunday Observer implies a kindly recognition that the Catholic Church is now at least of equal stature in England with the Protestant churches.

:: A tendency towards reciprocity implies that people will feel obligated to respond if someone helps them.

The assumption of unit-treatment addivity implies that, for every treatment, the th treatment have exactly the same effect on every experiment unit.

For a randomized experiment, the assumption of unit-treatment additivity implies that the variance is constant for all treatments.

" Thus Boolos and Jeffrey are saying that an algorithm implies instructions for a process that " creates " output integers from an arbitrary " input " integer or integers that, in theory, can be chosen from 0 to infinity.

The term allocution differs from distribution as distribution implies that the original party loses some kind of control over the information.

The statement of the axiom of choice does not specify whether the collection of nonempty sets is finite or infinite, and thus implies that every finite collection of nonempty sets has a choice function.

For example, while the axiom of choice implies that there is a well-ordering of the real numbers, there are models of set theory with the axiom of choice in which no well-ordering of the reals is definable.

Another argument against the axiom of choice is that it implies the existence of counterintuitive objects.

However, ZF plus GCH implies AC, making GCH a strictly stronger claim than AC, even though they are both independent of ZF.