it was noted by Bohr that the existence of any sort of wave packet implies uncertainty in the wave frequency and wavelength, since a spread of frequencies is needed to create the packet itself.

Although the Greek word " techně " is often mistranslated as " art ," it actually implies mastery of any sort of craft.

Since this process does not involve any heat transfer or work, the First Law of Thermodynamics then implies that the net internal energy change of the system is zero.

As the title implies, any active device received the sum of all transmitted messages in universal space-time, in a single pulse, so that demultiplexing yielded information about the past, present, and future.

The inability to comprehend any aspect of the thing other than its properties implies, this argument maintains, that one cannot conceive of a bare particular ( a substance without properties ), an implication that directly opposes substance theory.

The term Stone Age implies the inability to smelt any ore, the term Bronze Age implies the inability to smelt iron ore and the term Iron Age implies the ability to manufacture artifacts in any of the three types of hard material.

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.

Such equal consideration does not necessarily imply identical treatment of humans and non-humans, any more than it necessarily implies identical treatment of all humans.

This implies, by the Bolzano – Weierstrass theorem, that any infinite sequence from the set has a subsequence that converges to a point in the set.

It implies the ability to defend one ’ s interests and if necessary to impose one ’ s will by any means available.

This is because if a group has sectional 2-rank at least 5 then MacWilliams showed that its Sylow 2-subgroups are connected, and the balance theorem implies that any simple group with connected Sylow 2-subgroups is either of component type or characteristic 2 type.

This interpolation is not unique: aliasing implies that one could add N to any of the complex-sinusoid frequencies ( e. g. changing to ) without changing the interpolation property, but giving different values in between the points.

The doctrine implies that any attempt to depose the king or to restrict his powers runs contrary to the will of God and may constitute a sacrilegious act.

The doctrine implies that any attempt to depose the king or to restrict his powers runs contrary to the will of God and may constitute a sacrilegious act.

The above definition implies this one: the upper bound of the empty subset is any existing element of A, because A is nonempty ; furthermore, as provable with an induction argument over the size of nonempty finite subsets, the upper bound of a finite subset may be obtained by finding upper bounds of pairs iteratively.

Although siblinghood is symmetric ( if A is a sibling of B, then B is a sibling of A ) and transitive on any 3 distinct people ( if A is a sibling of B and C is a sibling of B, then A is a sibling of C, provided A is not C ( Note that " is a sibling of " is NOT a transitive relation, since A R B, and B R A implies A R A by transitivity )), it is not reflexive ( A cannot be a sibling of A ).

Another advantage of FIR filters is that their impulse response can be made symmetric, which implies a response in the frequency domain which has zero phase at all frequencies ( not considering a finite delay ), which is absolutely impossible with any IIR filter.

The existence of a complex derivative is a very strong condition, for it implies that any holomorphic function is actually infinitely differentiable and equal to its own Taylor series.

0 implies that any function f that is holomorphic on the simply connected region U is also integrable on U. ( For a path γ from z < sub > 0 </ sub > to z lying entirely in U, define

The holographic principle was inspired by black hole thermodynamics, which implies that the maximal entropy in any region scales with the radius squared, and not cubed as might be expected.

`` 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.

It implies two misconceptions.

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 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.