In mathematics, the absolute value ( or modulus ) of a real number is the numerical value of without regard to its sign.

The absolute value of a number may be thought of as its distance from zero.

For any real number the absolute value or modulus of is denoted by ( a vertical bar on each side of the quantity ) and is defined as

In addition, virtually an unlimited number of slots can be provided with 20, including the SBC slot, as a practical though not an absolute limit.

where is the difference in density of particles separated by a height difference of, is Boltzmann's constant ( namely, the ratio of the universal gas constant,, to Avogadro's number, ), and is the absolute temperature.

It is usual for a decimal number whose absolute value is less than one to have a leading zero.

However, in enlightened absolutism ( also known as benevolent despotism ), which came to prominence in 18th century Europe, absolute monarchs used their authority to institute a number of reforms in the political systems and societies of their countries.

An empirical formula makes no reference to isomerism, structure, or absolute number of atoms.

* Logarithmic number systems represent a real number by the logarithm of its absolute value and a sign bit.

Using their data on the time occupied by travel to work, Table 2 below shows the absolute number of people who responded with travel times " at least 15 but less than 20 minutes " is higher than the numbers for the categories above and below it.

That is, ƒ ( z ) is the absolute value ( or modulus ) of the complex number z.

Shannon's entropy represents an absolute limit on the best possible lossless compression of any communication, under certain constraints: treating messages to be encoded as a sequence of independent and identically distributed random variables, Shannon's source coding theorem shows that, in the limit, the average length of the shortest possible representation to encode the messages in a given alphabet is their entropy divided by the logarithm of the number of symbols in the target alphabet.

* The absolute value of a real or complex number ( | a | )

The race Directors retain the absolute discretion to exclude any horse from the race, or exempt any horse from the ballot on the race, but in order to reduce the field to the safety limit of 24, horses are balloted out based on a number of factors which include:

A non-zero element of an ordered field F is infinitesimal if and only if its absolute value is smaller than any element of F of the form 1 / n, for n a standard natural number.

Road safety in Russia is poor with road accident deaths per million population higher than all countries in the G8 and the other BRIC countries, although the absolute number is actually less than China, India and USA.

However, if no candidate receives the required number of votes ( usually an absolute majority or 40-45 % with a winning margin of 5-15 %), then those candidates having less than a certain proportion of the votes, or all but the two candidates receiving the most votes, are eliminated, and a second round of voting occurs.

If no candidate receives an absolute majority in the first round then the candidate ( s ) with the fewest number of votes is eliminated and excluded from further ballots.

Since the constitution of 1978 came into effect, there have not been any coalition governments, even if the party with the largest number of seats has failed to obtained absolute majority, though in such cases the party in government has had to rely on the support of minority parties to gain confidence and to approve the State's budgets.

The number of sunspots correlates with the intensity of solar radiation over the period since 1979, when satellite measurements of absolute radiative flux became available.

It gives the co-ordinates in 1900 epoch, the secular variation, the proper motion, the weighted average absolute parallax and its standard error, the number of parallax observations, quality of interagreement of the different values, the visual magnitude and various cross-identifications with other catalogues.

Alternate definitions are, " the entropy of all systems and of all states of a system is smallest at absolute zero ," or equivalently " it is impossible to reach the absolute zero of temperature by any finite number of processes ".

The absolute number of tuberculosis cases has been decreasing since 2006, and new cases have decreased since 2002.

The Cochrane Collaboration ( 2011 ) concluded that mammograms reduce mortality from breast cancer by a absolute amount of 0. 05 % or and relative amount of 15 %, but also result in unnecessary surgery and anxiety, resulting in their view that it is not clear whether mammography screening does more good or harm.

Uncontrolled metastatic cancer outside liver, active drug or alcohol abuse and active septic infections are absolute contraindications.

" It's for a single issue that's of absolute critical importance to all the people in Thunder Bay and northwestern Ontario, and that's the cancer research centre ", he said.

A high amylase level ( twice the serum level or the absolute value is greater than 160 Somogy units ) in the pleural fluid is indicative of either acute or chronic pancreatitis, pancreatic pseudocyst that has dissected or ruptured into the pleural space, cancer or esophageal rupture.

In Evangelium Vitae, Pope John Paul II suggested that capital punishment should be avoided unless it is the only way to defend society from the offender in question, opining that punishment " ought not go to the extreme of executing the offender except in cases of absolute necessity: in other words, when it would not be possible otherwise to defend society.

It is possible in rare cases that two substituents on an atom differ only in their absolute configuration ( R or S ).

The masking threshold is calculated using the absolute threshold of hearing and the principles of simultaneous masking — the phenomenon wherein a signal is masked by another signal separated by frequency, and, in some cases, temporal masking — where a signal is masked by another signal separated by time.

Some of the characteristics of a presidential system ( i. e., a strong dominant political figure with an executive answerable to them, not the legislature ) can also be found among absolute monarchies, parliamentary monarchies and single party ( e. g. Communist ) regimes, but in most cases of dictatorship, their stated constitutional models are applied in name only and not in political theory or practice.

In both cases the praise was limited, with Cerruti going on to write that only in the Third Reich was it possible for someone as superficial as Ribbentrop to rise to be a minister of foreign affairs, while Geyr von Schweppenburg called Ribbentrop an absolute disaster as Ambassador in London.

The rule of Miranda is not, therefore, absolute and can be a bit more elastic in cases of public safety.

These belief systems hold that the Creator ( or, in some cases, Nature or Evolution ) has fashioned a system of absolute freedom: human volition that features a free and independent nature.

However, as noted above in cases where there are 3 or more strong candidates, runoff voting will sometimes produce an absolute majority for a different winner than the candidate elected by the other two.

In all cases, absolute coordinates follow capital letter commands and relative coordinates are used after the equivalent lower-case letters.

In many cases the state is short-lived, even when cooled to near absolute zero.

for absolute black body and is generally greater than 1 for other cases.

In certain cases, such as the Great Leap Forward in China ( which produced the largest famine in absolute numbers ), North Korea in the mid-1990s, or Zimbabwe in the early-2000s, famine can occur because of government policy.

In reality, however in all cases the state governments have an absolute ability to overrule the local decision-making.

There is some evidence for vowel harmony according to vowel height or ATR in the prefix i < sub > 3 </ sub >/ e-in inscriptions from pre-Sargonic Lagash ( the specifics of the pattern have led a handful of scholars to postulate not only an / o / phoneme, but even an and, most recently, an ) Many cases of partial or complete assimilation of the vowel of certain prefixes and suffixes to one in the adjacent syllable are reflected in writing in some of the later periods, and there is a noticeable though not absolute tendency for disyllabic stems to have the same vowel in both syllables.

Antigone responds with the idea that state law is not absolute, and that it can be broken in civil disobedience in extreme cases, such as honoring the gods, whose rule and authority outweigh Creon's.

:: Subsequent absolute tautonymy ( only very few cases )

In all cases — real distinct eigenvalues, real duplicated eigenvalues, and complex conjugate eigenvalues — the equation is stable ( that is, the variable a converges to a fixed value ( specifically, zero )); if and only if both eigenvalues are smaller than one in absolute value.

One is glory, determined by either work or procreation, and the other the asceticism of religion or magic — both, Călinescu believed, where aimed at reaching the absolute, even in those cases where Eliade described the latter as an " abyssal experience " into which man may take the plunge.

There may be particular instances or cases of these laws, but we could never get the laws themselves in their universality, far less absolute impersonality.

* the upper culmination is above, and the lower below the horizon, so the body is observed to rise and set daily ; in the other cases ( i. e. if in absolute value the declination is less than the colatitude )