Most acids encountered in everyday life are aqueous solutions, or can be dissolved in water, and these two definitions are most relevant.

This topic was further developed in the 1930s by Alonso Church and Alan Turing, who on the one hand gave two independent but equivalent definitions of computability, and on the other gave concrete examples for undecidable questions.

The choice between the two definitions usually matters only in very formal contexts, like category theory.

Because these two definitions can be transformed simply by into the other, some formulae have this alternatingly (- 1 )< sup > n </ sup >- term and others not depending on the context, but it is not possible to decide in favor of one of these definitions to be the correct or appropriate or natural one ( for the abstract Bernoulli numbers ).

Whenever a confusion between the two kinds of definitions might arise it can be avoided by referring to the more general definition and by reintroducing the erased parameter: writing B < sub > m </ sub >( 0 ) in the first case and B < sub > m </ sub >( 1 ) in the second will unambiguously denote the value in question.

Love's song lyrics are predominantly told from a female's point of view, and her earlier work, particularly on Hole's first two albums, was noted for being highly aggressive and critical toward cultural definitions of women.

The difference between the two definitions is that under the former, finite sets are also considered to be countable, while under the latter definition, they are not considered to be countable.

There are two similar definitions that are equivalent:

If the possibility of adding the empty string to a language is added to the strings recognized by the noncontracting grammars ( which can never include the empty string ) then the languages in these two definitions are identical.

The two perhaps most popular definitions used in older literature are the 15 ° C calorie and the thermochemical calorie.

The differential map provides the link between the two alternate definitions of the cotangent bundle given above.

One can show that this map is an isomorphism, establishing the equivalence of the two definitions.

If the axiom of choice is assumed, as will be the case in the rest of this article, then the two definitions are equivalent.

For example, consider these two definitions:

The constant definitions at the end show two assembler features: the assembler radix is octal by default (< tt > 20 </ tt >

Under Java or C ++ the visibility of an object is defined in the code itself, meaning that to support a similar change the programmer would be forced to re-write the definitions completely, and could not have two versions at the same time.

In particular we may use either of the two following definitions which are equivalent.

There are two related definitions of entropy: the thermodynamic definition and the statistical mechanics definition.

According to the Merriam-Webster Dictionary, the term has two distinct definitions in modern English.

Thus, the definiendum in such definitions is always a species ( and not an individual ), while the definiens consists of two parts:

For example, consider these two definitions:

Those definitions can be expressed as one genus and two differentiae:

A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another ; see graph ( mathematics ) for more detailed definitions and for other variations in the types of graph that are commonly considered.

Because entropy can be conditioned on a random variable or on that random variable being a certain value, care should be taken not to confuse these two definitions of conditional entropy, the former of which is in more common use.

But in our case -- and neither my wife nor I have extreme views on integration, nor are we given to emotional outbursts -- the situation has ruined one or two valued friendships and come close to wrecking several more.

The two main charges levelled against the Bourbons by liberals is that they are racists and social reactionaries.

( There are two receivers in case one should be dropped and damaged.

It seems that for Persia, and especially for this city, there are only two times: the glorious past and the corrupt, depressing, sterile present.

The one apparent connection between the two is a score of buildings which somehow or other have survived and which naturally enough are called `` historical monuments ''.

These songs ( practically all Persian music, for that matter ) are limited to a range of two octaves.

Here are the two Preambles: Federal Constitution, 1789

Whatever pole of this contrast one emphasizes and whatever the tension between these two approaches to understanding the artistic imagination, it will be readily seen that they are not mutually exclusive, that they belong together.

But people can't be made to integrate, socialize ( the two are inseparable by Southern standards ) by law.

Of these there are surely few that would be more rewarding discoveries than Verner Von Heidenstam, the Swedish poet and novelist who received the award in 1916 and whose centennial was celebrated two years ago.

In the mystery story, as in The Wealth of Nations, individualism and the social good are two sides of the same benevolent coin.

So all-important are ideas, we are told, that persons successful in business and happy in social life usually fall into two classes: those who invent new ideas of their own, and those who borrow, beg, or steal from others.

These ways are absolutely irreconcilable because they offer two different recipes for man's redemption from chaos.

Within this context of spontaneous and unanalyzed responses to the experience of civilizational crisis, two basic organizations of response are observable: reaction and ideological progressivism.

There is probably some significance in the fact that two of the best incest stories I have encountered in recent years are burlesques of the incest myth.

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.

`` the matters to be considered are obviously of a grave character, and I therefore respectfully request that the hearing be postponed for two weeks in order that I might make adequate preparation ''.

Office workers frequently go out there to lunch and swim during the siesta period, which, during the summer, lasts from two until five in the afternoon, when shops and offices are again open for business.

But there are at least two reasons for contemplating one's mind in even a cracked mirror.

There are only two men remaining in Congress who, with Rayburn, voted for the declaration of war against Germany in 1917.

Regardless of the decision two facts are clear.

Some brilliant rookies nailed them down, so that this spring just two spots, left and right field, are really up for grabs.

The speed is controlled by pressing on the two brake buttons located where the index finger and thumb are placed when holding the motor.

The biggest nuclear device the United States has exploded measured some 15 megatons, although our B-52s are said to be carrying two 20-megaton bombs apiece.