* 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.

It then follows that Af is large enough, but this is not obvious from the above expression.

Thus, the above conditions could be re-written as follows:

We know that is opaque and thus follows that is opaque, so in the above equation, each operator can be written as a convex combination:

where is the Gelfand representation of x defined as follows: is the continuous function from Δ ( A ) to C given by The spectrum of in the formula above, is the spectrum as element of the algebra C ( Δ ( A )) of complex continuous functions on the compact space Δ ( A ).

In what follows the dates are as given in the Chronicle, although as noted above, these are earlier than now thought accurate.

From the above rule of calculation of heat with respect to volume, there follows one with respect to pressure.

The corners are named as follows ( the numbers correspond to the image above, starting at the start / finish line ):

* Falling putts ( when the player follows through described above on a putt 10 meters or shorter ) and foot faults ( when a player does not release the disc behind their mark or within the required distance of the mark, when a player has a part of their body touching the ground on release past their mark or when their tee shot is released from off the teeing area ) are penalized in a unique way.

Based on the above, the number of revelations ( accounting for sections that are not revelations ) presented by each Community of Christ prophet, are as follows:

This article follows the above working definition.

Given a groupoid G, the vertex groups or isotropy groups or object groups in G are the subsets of the form G ( x, x ), where x is any object of G. It follows easily from the axioms above that these are indeed groups, as every pair of elements is composable and inverses are in the same vertex group.

By contrast, the yarn in knitted fabrics follows a meandering path ( a course ), forming symmetric loops ( also called bights ) symmetrically above and below the mean path of the yarn.

The Klein bottle can be seen as a fiber bundle over S < sup > 1 </ sup > as follows: one takes the square ( modulo the edge identifying equivalence relation ) from above to be E, the total space, while the base space B is given by the unit interval in y, modulo 1 ~ 0.

This story can be translated to Adam's stopping rule above, as follows.

This rule requires the court to take the facts as the accused believed them to be and follows Hadfield's Trial, above.

from which the strategy above follows by the Sprague – Grundy theorem.

Since E < sub > 2 </ sub >-E < sub > 1 </ sub > ≫ kT, it follows that the argument of the exponential in the equation above is a large negative number, and as such N < sub > 2 </ sub >/ N < sub > 1 </ sub > is vanishingly small ; i. e., there are almost no atoms in the excited state.

The above formula can also be re-written in terms of a Composite Risk Index, as follows:

From the above stated equations it can be expressed as follows:

( Note that the choice of signs for above follows the space-like convention (−+++).

But since ( as above ) this statement is logically equivalent to ( 1 ) all ravens are black, it follows that the sight of a green apple is evidence supporting the notion that all ravens are black.

Once converted, it follows the same pathway as described above.

A Clifford algebra as described above always exists and can be constructed as follows: start with the most general algebra that contains V, namely the tensor algebra T ( V ), and then enforce the fundamental identity by taking a suitable quotient.

The uncountability of the real numbers was already established by Cantor's first uncountability proof, but it also follows from the above result.