* The rational numbers, expressed as the quotient of two integers a and b, b not equal to zero, satisfy the above definition because is the root of.

Prisms and antiprisms, whose symmetry groups are the dihedral groups, are generally not considered to be Archimedean solids, despite meeting the above definition.

In fact anode polarity depends on the device type, and sometimes even in which mode it operates, as per the above electric current direction-based universal definition.

From the above, it is possible to reformulate the definition to either of the following:

There is a larger class of number-theoretic functions that do not fit the above definition, e. g. the prime-counting functions.

According to the definition above, two relations with the same graph may be different, if they differ in the sets and.

Because this range of non-zero amplitude may be very broad or infinite, this definition is typically relaxed so that the bandwidth is defined as the range of frequencies in which the signal's spectral density is above a certain threshold relative to its maximum.

Although sometimes referred to as a coalition government, according to the definition above, it was not.

The above definition imposes no constraints on η ( 0 ), even though it is assumed that η ( k ) tends to zero as k tends to zero.

Because the above expression is equal to the difference, by the definition of the derivative is differentiable at a and its derivative is f ′( g ( a )) g ′( a ).

In practice, the above definition is rarely used because in virtually all cases, the curl operator can be applied using some set of curvilinear coordinates, for which simpler representations have been derived.

The informal definition above is subject to a rounding problem called the table-maker's dilemma whereas the modern definition is not.

First, State coercion may very easily be arbitrary – indeed technically very specific, according to the above definition.

Given the definition of above, we might fix ( or ' bind ') the first argument, producing a function of type.

The above definition of the commutator is used by some group theorists.

The above definition of the conjugate of a by x is used by some group theorists.

A nominal definition is the definition explaining what a word means, i. e. which says what the ' nominal essence ' is, and is definition in the classical sense as given above.

The four definitions given above are special cases of a more general definition.

Famine is classified by Rummel as democide if it fits the definition above.

In this case the definition above has no explicit instructions, so in both languages access to the slots and methods is considered, meaning they can be used only by subclasses.

In addition to the definition above, there is an equivalent definition.

`` 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.

Just as the physical bodies of people are changed into spiritual bodies in the resurrection ( see above ), so Isaiah implies that animals will undergo a transformation which enables them to live in peace with human beings and with each other.

Despite the above, the noun form in English (" attendant ") is someone who waits on another, generally with menial tasks and in a temporary fashion, as on an airplane or hotel ; whereas ' assistant ' implies a longer-term, higher level, and often contractual (= employment ), relationship.

An analysis of supply and demand of the type shown in introductory mainstream economics textbooks implies that by mandating a price floor above the equilibrium wage, minimum wage laws should cause unemployment .< ref name = MB > McConnell, C. R.

This phenomenon is also associated with a changing speed of light as seen from the definition of index of refraction provided above which implies:

Every quark in the universe does not attract every other quark in the above distance independent manner, since colour-confinement implies that the strong force acts without distance-diminishment only between pairs of single quarks, and that in collections of bound quarks ( i. e., hadrons ), the net colour-charge of the quarks cancels out, as seen from far away.

This generalized definition implies that the above mentioned geometric entities are a special kind of vectors, as they are elements of a special kind of vector space called Euclidean space.

According to the relations, given above, this implies also small current and voltage variations.

Consequently, the above theorem implies that:

Note in the above example that shoigeg does not have the same meaning in Yeshivish as it does in its original context, wherein it implies negligence.

It may be noted that the above equation implies that gravitational acceleration is a constant over z since it is placed outside of the integral.

This implication is significant for practical reasons because it implies that central banks should not set employment targets above the natural rate.

As the name implies, Chalvey lies low on the plain of the River Thames and there may have been enough of a rise for an island to stand above the slough from which the later town takes its name.

The definition implies that the scientific explanation of the world around us is the ' normal ' part of the word and ' para ' makes up the above, beyond, beside, contrary, or against part of the meaning.

" In the 7th edition ( 1845 ) it still implies a definite social status: " All above the rank of yeomen.

This meaning is also false when applied to God, because it implies likening something to God, whereas God is above all likeness.

This method of gradualism implies utilization of the existing state apparatus and machinery of government to gradually move society toward socialism, and is sometimes derided by other socialists as a form of " socialism from above " or political " elitism " for relying on electoral means to achieve socialism.

The former implies the ability to ( re ) create a sensation of sounds coming from above the listener, and / or a sensation of space above the listener.

Oceanic crust has a layered velocity structure that implies a layered rock series similar to that listed above.

Combining the above two theorems implies that Hodge conjecture is true for Hodge classes of degree 2n − 2.

* A shake on a brass instrument, especially the trumpet, implies quickly slurring to a note above the written note

In particular, using the above description of the Lie algebra cso ( 1, 1 ), this implies that

His situation implies great trust ; he is responsible for the mistakes, negligences, and ignorances of those he employs ; and above all, he is to take care that the workmen's bills do not exceed his own estimates.