The Northeastern limit of the Sea of Marmara line joining Cape Rumili with Cape Anatoli ( 41 ° 13 ' N ).

The International Hydrographic Organization defines the western limit of the Gulf of Finland as a line running from Spithami ( 59 ° 13 ' N ), in Estonia, through the island of Osmussaar from SE to NW and on to the SW extreme of Hanko Peninsula ( 22 ° 54 ' E ) in Finland.

The Northern limit of the Arabian Sea line joining Ras al Hadd | Ràs al Hadd, East point of Arabia ( 22 ° 32 ' N ) and Jiwani | Ràs Jiyùni ( 61 ° 43 ' E ) on the coast of Pakistan < nowiki ></ nowiki >.

* The Monster of Compression benchmark by N. F. Antonio tests compression on 1Gb of public data with a 40 minute time limit.

First, the elements C, N and O are only created after at least one cycle of star birth / death: this is a limit to the earliest time life could have arisen.

However, the scientists noted that phosphate ( PO < sub > 4 </ sub >) and nitrate ( NO < sub > 3 </ sub >– N ) criticaly limit nutrition to many terrestrial lifeforms.

Given an arbitrary group G, there is a related profinite group G < sup >^</ sup >, the profinite completion of G. It is defined as the inverse limit of the groups G / N, where N runs through the normal subgroups in G of finite index ( these normal subgroups are partially ordered by inclusion, which translates into an inverse system of natural homomorphisms between the quotients ).

This limit is defined as " A line joining Ràs Limah ( 25 ° 57 ' N ) on the coast of Arabia and Ràs al Kuh ( 25 ° 48 ' N ) on the coast of Iran ( Persia )".

The area can be defined as north of the Arctic Circle ( 66 ° 33 ' N ), the approximate limit of the midnight sun and the polar night.

A limit of the diagram F: J → C is a cone ( L, φ ) to F such that for any other cone ( N, ψ ) to F there exists a unique morphism u: N → L such that φ < sub > X </ sub > o u =

One can use the above relationship to define the limit of F in C. The first step is to observe that the limit of the functor Hom ( N, F –) can be identified with the set of all cones from N to F:

Identifying the limit of Hom ( F –, N ) with the set Cocone ( F, N ), this relationship can be used to define the colimit of the diagram F as a representation of the functor Cocone ( F, –).

A line running from Cape Negrais ( 16 ° 03 ' N ) in Burma through the larger islands of the Andaman group, in such a way that all the narrow waters between the islands lie to the Eastward of the line and are excluded from the Bay of Bengal, as far as a point in Little Andaman Island in latitude 10 ° 48 ' N, longitude 92 ° 24 ' E and thence along the Southwest limit of the Burma Sea

The Eastern limit of the Bay of Bengal line running from Cape Negrais ( 16 ° 03 ' N ) in Burma through the larger islands of the Andaman Islands | Andaman group, in such a way that all the narrow waters between the islands lie to the Eastward of the line and are excluded from the Bay of Bengal, as far as a point in Little Andaman Island.

The Northeastern limit of the Eastern China Sea Nomo Saki ( 32 ° 35 ' N ) in Kyūshū | Kyusyu to the South point of Fukuejima | Hukae Sima ( Gotō Islands | Goto Retto ) and on through this island to Ose Saki ( Cape Goto ) and to Hunan Kan, the South point of Jeju-do | Saisyu To ( Quelpart ), through this island to its Western extreme and thence along the parallel of 33 ° 17 ' North to the mainland and the Western limit of the Inland Sea circuitously as " The Southeastern limit of the Japan Sea ".

In the case of integer order n, the function is defined by taking the limit as a non-integer α tends to n:

The latter is the difference quotient for g at a, and because g is differentiable at a by assumption, its limit as x tends to a exists and equals g ′( a ).

In their native habitats, the toads can be found in subtropical forests, although dense foliage tends to limit their dispersal.

For example, the cofinality of ω² is ω, because the sequence ω · m ( where m ranges over the natural numbers ) tends to ω² ; but, more generally, any countable limit ordinal has cofinality ω.

The limit is the result of letting h go to zero, meaning it is the value that tends to as h becomes very small:

The cost of good hard cases — USD 500 to over USD 2500 — tends to limit their use to touring professionals.

Children can hear some high-pitched sounds that older adults cannot hear, because in humans the upper limit pitch of hearing tends to become lower with age.

Animated cartoon films are typically made at reduced frame rates ( accomplished by shooting several film frames of the individual drawings ) so as to limit production costs, with the result that jerkiness tends to be apparent.

Lebesgue presents six conditions which it is desirable that the integral should satisfy, the last of which is " If the sequence f < sub > n </ sub >( x ) increases to the limit f ( x ), the integral of f < sub > n </ sub >( x ) tends to the integral of f ( x ).

Criminal penalties thus tends to limit the supply more than the demand, driving up the black-market price and creating monopoly profits for those criminals who remain in business.

1, which is the limit of f as z tends to 0.

While the creation of the built environment can act as a form of crisis displacement, it can also constitute a limit in its own right, as it tends to freeze productive forces into a fixed spatial form.

Although early reduction of placental development is not accompanied by concurrent reduction of fetal growth ; it tends to limit fetal growth later in gestation.

The quantity e < sup > y </ sup > can be found by taking the limit on both sides as n tends to infinity and using Wallis ' product,

In the limit of infinitely slow performance, the dissipation tends to zero and then the limiting process, though fictional rather than actual, is notionally reversible, and is called quasi-static.

This design tends to limit the usable height to how long the loader arm is and the height of that pivot point.

Since they operate for-profit, commercial organizations also cannot spend an unlimited amount on precautions and remain competitive-a commercial context tends to limit privacy measures, and to motivate organizations to share data when working in partnership.

In the limit of low frequencies ( i. e. long wavelengths ), Planck's law becomes the Rayleigh – Jeans law, while in the limit of high frequencies ( i. e. small wavelengths ) it tends to the Wien approximation.

In the limit as dt tends to 0, the dt < sup > 2 </ sup > and dt dB terms disappear but the dB < sup > 2 </ sup > term tends to dt.

Note that the limit as n tends to infinity exists if.

For large sample sizes, the central limit theorem says this distribution tends toward a certain multivariate normal distribution.

* An example of a non-unitary associative algebra is given by the set of all functions f: R → R whose limit as x nears infinity is zero.

( To be precise: for the definition of the dipole moment one should always consider the " dipole limit ", where e. g. the distance of the generating charges should converge to 0, while simultaneously the charge strength should diverge to infinity in such a way that the product remains a positive constant.

The expected value may be intuitively understood by the law of large numbers: the expected value, when it exists, is almost surely the limit of the sample mean as sample size grows to infinity.

The order ( at infinity ) of an entire function f ( z ) is defined using the limit superior as:

Such a limit is possible only in mathematical settings, where accurate repetitions unto infinity may be made ( e. g. such as counting the relative fraction of even numbers less than n < sub > t </ sub >: one may easily compute the limit.

For exponents equal to positive or negative infinity the means are maximum and minimum, respectively, regardless of weights ( and they are actually the limit points for exponents approaching the respective extremes ):

In the case of tossing a fair coin, frequentists say that the probability of getting a heads is 1 / 2, not because there are two equally likely outcomes but because repeated series of large numbers of trials demonstrate that the empirical frequency converges to the limit 1 / 2 as the number of trials goes to infinity.

The prime number theorem then states that the limit of the quotient of the two functions π ( x ) and x / ln ( x ) as x approaches infinity is 1, which is expressed by the formula

This notation ( and the theorem ) does not say anything about the limit of the difference of the two functions as x approaches infinity.

His work is notable for the use of the zeta function ζ ( s ) ( for real values of the argument " s ", as are works of Leonhard Euler, as early as 1737 ) predating Riemann's celebrated memoir of 1859, and he succeeded in proving a slightly weaker form of the asymptotic law, namely, that if the limit of π ( x )/( x / ln ( x )) as x goes to infinity exists at all, then it is necessarily equal to one.

By explaining past changes by analogy with present phenomena, a limit is set to conjecture, for there is only one way in which two things are equal, but there are an infinity of ways in which they could be supposed different.

The case where u is required to vanish at an endpoint is the limit of this condition when the respective a or b approaches infinity.

The upper limit of this integral can be extended to infinity as well if one defines for < math >

The limit, for n going to infinity, is zero.

Much of WMCF deals with the important concepts of infinity and of limit processes, seeking to explain how finite humans living in a finite world could ultimately conceive of the actual infinite.

In the limit, as n goes to infinity, the limit of the sum of the powers of 4 / 9 is 4 / 5, so

* f has a limit at infinity ( either ∞ or −∞) of either a real number, ∞, or −∞.

By adjoining the elements +∞ and −∞ to R, we allow a formulation of a " limit at infinity " with topological properties similar to those for R.

The upper limit of this integral can be extended to infinity as well if one defines χ ( Δt ) = 0 for Δt < 0.

The present value of a perpetuity can be calculated by taking the limit of the above formula as n approaches infinity.

The limit of the reduced mass formula as one mass goes to infinity is the smaller mass, thus this approximation is used to ease calculations, especially when the larger particles exact mass is not known.

The harmonic series is counterintuitive to students first encountering it, because it is a divergent series though the limit of the nth term as n goes to infinity is zero.