`` That limit has now been reached ''.

In the common law, an answer is the first pleading by a defendant, usually filed and served upon the plaintiff within a certain strict time limit after a civil complaint or criminal information or indictment has been served upon the defendant.

The government has undertaken regulatory reforms in some areas, including substantial opening of trade policy, but inefficient public administration in which commercial and regulatory interests are co-mingled limit the impact of these reforms.

There are techniques of anchoring to limit the swing of a vessel if the anchorage has limited room:

In 1931, Subrahmanyan Chandrasekhar calculated, using special relativity, that a non-rotating body of electron-degenerate matter above a certain limiting mass ( now called the Chandrasekhar limit at 1. 4 solar masses ) has no stable solutions.

If α is an integer, the limit has to be calculated.

However, following bad sales of Dark Void and Bionic Commando, the company's management has decided to limit outsourcing to sequels and newer versions of installments in existing franchises, reserving the development of original titles for its in-house teams.

In places the line's speed limit has been raised from to, and plans have been made to raise this further to on certain sections.

There was speculation at the time, however, that the NSA has deliberately reduced the key size from the original value of 112 bits ( in IBM's Lucifer cipher ) or 64 bits ( in one of the versions of what was adopted as DES ) so as to limit the strength of encryption available to non-US users.

This is totally spurious, since no matter who measured first the other will measure the opposite spin despite the fact that ( in theory ) the other has a 50 % ' probability ' ( 50: 50 chance ) of measuring the same spin, unless data about the first spin measurement has somehow passed faster than light ( of course TI gets around the light speed limit by having information travel backwards in time instead ).

Under the plan which starts within 90 days, Bell will be able to charge wholesale service providers a flat monthly fee to connect to its network, and for a set monthly usage limit per each ISP customer the ISP has.

On the one hand, Bernard Bolzano ( 1817 ) had been aware that any bounded sequence of points ( in the line or plane, for instance ) has a subsequence that must eventually get arbitrarily close to some other point, called a limit point.

# Every sequence in A has a convergent subsequence, whose limit lies in A.

# Every infinite subset of A has at least one limit point in A.

The customary acceptance of the fact that any real number x has a decimal expansion is an implicit acknowledgment that a particular Cauchy sequence of rational numbers ( whose terms are the successive truncations of the decimal expansion of x ) has the real limit x.

And in fact, since the 120 limit was enacted, no conclave has been held with even a full 120 entitled to participate.

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.

It has been inferred that as the white dwarf's mass approaches the Chandrasekhar limit, its central density increases, and, as a result of compressional heating, its temperature also increases.

Rabbi Milton Steinberg wrote that " By its nature Judaism is averse to formal creeds which of necessity limit and restrain thought " and asserted in his book Basic Judaism ( 1947 ) that " Judaism has never arrived at a creed.

For real values of, we have and for purely imaginary we have hence has a limit at 0 ( i. e., ƒ is complex differentiable at 0 ) if and only if.

In mathematical analysis, a metric space M is called complete ( or a Cauchy space ) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M.

In the first case, ƒ ( x ) has y = c as asymptote when x tends to −∞, and in the second that ƒ ( x ) has y = c as an asymptote as x tends to +∞

For example, the function has a horizontal asymptote at y = 0 when x tends both to −∞ and +∞ because, respectively,

The set of rational numbers descending from a node q is defined by the open interval ( L < sub > q </ sub >, H < sub > q </ sub >) where L < sub > q </ sub > is the ancestor of q that is smaller than q and closest to it in the tree ( or L < sub > q </ sub > = 0 if q has no smaller ancestor ) while H < sub > q </ sub > is the ancestor of q that is larger than q and closest to it in the tree ( or H < sub > q </ sub > = +∞ if q has no larger ancestor ).

An example is ƒ ( x ) = x − 1 / x, which has the oblique asymptote y = x ( m = 1, n = 0 ) as seen in the limits

More generally, if ƒ has a branch-point near the origin of such a nature that then

A function ƒ that has an inverse is called invertible ; the inverse function is then uniquely determined by ƒ and is denoted by ƒ < sup >− 1 </ sup > ( read f inverse, not to be confused with exponentiation ).

Specifically, if ƒ is an invertible function with domain X and range Y, then its inverse ƒ < sup >− 1 </ sup > has domain Y and range X, and the inverse of ƒ < sup >− 1 </ sup > is the original function ƒ.

This has the reasonable meaning that " IF for all values of x the truth-values of the functions φ and ψ of x are equivalent, THEN the function ƒ of a given φẑ and ƒ of ψẑ are equivalent.

Pick a point x in M. A derivation at x is a linear map D: C < sup >∞</ sup >( M ) → R which has the property that for all ƒ, g in C < sup >∞</ sup >( M ):

In mathematics, a singular function is any function ƒ defined on the interval b that has the following properties:

As a quite direct consequence of the above definition, and of the rules of formal derivation, one has, for any ƒ and g in K (( X ))

If the set of zeros of an analytic function ƒ has an accumulation point inside its domain, then ƒ is zero everywhere on the connected component containing the accumulation point.

As an example, the field of real numbers is not algebraically closed, because the polynomial equation x < sup > 2 </ sup > + 1 = 0 has no solution in real numbers, even though all its coefficients ( 1 and 0 ) are real.

If F is algebraically closed and p ( x ) is an irreducible polynomial of F, then it has some root a and therefore p ( x ) is a multiple of x − a.

Each of these hymns has eight four-line stanzas and is written in strict iambic dimeter ( that is 2 x 2 iambs ).

For example, the parent function y = 1 / x has a horizontal and a vertical asymptote, and occupies the first and third quadrant, and all of its transformed forms have one horizontal and vertical asymptote, and occupies either the 1st and 3rd or 2nd and 4th quadrant.

If a Banach algebra has unit 1, then 1 cannot be a commutator ; i. e., for any x, y ∈ A.

But Y < sub > α </ sub >( x ) has more meaning than that.

Bessel himself originally proved that for non-negative integers n, the equation J < sub > n </ sub >( x ) = 0 has an infinite number of solutions in x.

In Western countries, a bead frame similar to the Russian abacus but with straight wires and a vertical frame has been common ( see image ).

# An adiabat looks similar to an isotherm, except that during an expansion, an adiabat loses more pressure than an isotherm, so it has a steeper inclination ( more vertical ).

The most common coordinate system to use is the Cartesian coordinate system, where each point has an x-coordinate representing its horizontal position, and a y-coordinate representing its vertical position.

A rational function has at most one horizontal asymptote or oblique ( slant ) asymptote, and possibly many vertical asymptotes.

This protection explains why fossils preserved further from the Cathedral Formation are impossible to work with — tectonic squeezing of the beds has produced a vertical cleavage that fractures the rocks, so they split perpendicular to the fossils.

It also has a short, bristly and vertical brown ridge of hair along the spine from the shoulder to the rump ; the white stripes run into this ridge.

Dennis the Menace's famous ' red and black ' jersey had formed the colours of a few of the Beano characters ' clothes ( Minnie the Minx has the same, although the placement of the stripes is a bit different ; Ball Boy's was a vertical red and black ; Roger the Dodger has a chessboard design top, and Danny ( from the Bash Street Kids ) has a similar cap ), but they have changed for Minnie and Ball Boy ( Minnie at one point had a red and yellow top and Ball Boy's strip is now black and blue ).

It has a large flat-plate turret with slightly chamfered sides, vertical rear and very chmfered front and a large A-frame crane on the front of the turret.

In this case, the curve has vertical asymptotes and this limits the span to πc.

A revolving door normally has several wings / leaves that hang on a central shaft forming compartments which rotate one way about a vertical axis.

The tropical Atlantic ocean experiences depressed activity due to increased vertical wind shear across the region during El Niño years .< ref > On the flip side however, the tropical Pacific Ocean east of the dateline has above normal activity during El Niño years due to well above average water temperatures and decreased windshear.

If any part of the ball reaches any part of the imaginary vertical plane transected by this line while in-bounds and in possession of a player whose team is striving toward that end of the field, this is considered a touchdown and scores six points for the team whose player has advanced the ball to, or recovered the ball in, this position.

* There are many examples of centuries-old glass shelving which has not bent, even though it is under much higher stress from gravitational loads than vertical window glass.

The giraffe has an extremely elongated neck, which can be up to in length, accounting for much of the animal's vertical height.

For all pictures the magnetic quantum number m has been set to 0, and the cross-sectional plane is the xz-plane ( z is the vertical axis ).

The traditional stand has the pedal almost directly below the cymbals, which are supported by a hollow vertical tube.

Chrysler Jeep claims it has the exclusive rights to use the seven vertical slits since it is the sole remaining assignee of the various companies since Willys gave their postwar jeeps seven slots instead of Ford's nine-slot design for the Jeep.

Each such fabric has different properties: a garter stitch has much more vertical stretch, while ribbing stretches much more horizontally.