More generally, suppose that an experiment consists of a number of independent trials, that each trial results in either a `` success '' or a `` non-success '' ( `` failure '' ), and that the probability of success remains constant from trial to trial.

More generally, in a k-dimensional array, the address of an element with indices i < sub > 1 </ sub >, i < sub > 2 </ sub >, …, i < sub > k </ sub > is

More recently, an abettor is generally known as an accomplice.

More expensive pigments are generally replicated by hues.

More generally, one curve is a curvilinear asymptote of another ( as opposed to a linear asymptote ) if the distance between the two curves tends to zero as they tend to infinity, although usually the term asymptote by itself is reserved for linear asymptotes.

More generally, as noted by A. W.

More generally, a binary relation between two sets A and B is a subset of.

More generally, a new component is said to be backward compatible if it provides all of the functionality of the old component.

More generally, an n-piece cubic Bézier curve can approximate a circle, when each inner control point is the distance from an outer control point on a unit circle, where t is 360 / n degrees, and n > 2.

More generally, every C *- algebra is a Banach algebra.

More generally, a series

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

More generally, calculus ( plural calculi ) refers to any method or system of calculation guided by the symbolic manipulation of expressions.

More generally, many philosophers and scientists have been unhappy about the difficulty of producing a definition that does not involve circularity or fuzziness.

More broadly, philosophers who do not accept the possibility of zombies generally believe that consciousness is reflected in behavior ( including verbal behavior ), and that we attribute consciousness on the basis of behavior.

Among the teachings of Jesus Christ in the Gospel of Luke and the Gospel of Matthew, the message to his followers that one should " Turn the other cheek " and his example in the story Pericope Adulterae, in which Jesus intervenes in the stoning of an adulteress, are generally accepted as his condemnation of physical retaliation ( though most scholars agree that the latter passage was " certainly not part of the original text of St John's Gospel ") More militant Christians consider Romans 13: 3 – 4 to support the death penalty.

* More generally, compact groups such as an orthogonal group are compact, while groups such as a general linear group are not.

More generally, compact sets can be separated by open sets: if K < sub > 1 </ sub > and K < sub > 2 </ sub > are compact and disjoint, there exist disjoint open sets U < sub > 1 </ sub > and U < sub > 2 </ sub > such that and.

More generally, electric current can be represented as the rate at which charge flows through a given surface as:

More generally, the idea of a contractive mapping can be defined for maps between metric spaces.

More generally, unspecific coercion may be the form taken by disciplinary coercion, and this appears to be in fact the case within the most effective command systems of the modern world.

More generally, judges look at the difficulty and execution of jumps, stunts and tumbling, synchronization, creativity, the sharpness of the motions, showmanship, and overall routine execution.

More generally among Baptists, a variety of parachurch agencies and evangelical educational institutions may be supported generously or not at all, depending entirely upon the local congregation's customs and predilections.

More generally, one can consider finite direct sums of matrix algebras.

More generally, inheritance now is quite different than those in the past.

More explicitly, it is stating that for every indexed family of nonempty sets there exists an indexed family of elements such that for every.

More specifically, every morphism in C must be assigned to a morphism in D. In other words, a contravariant functor acts as a covariant functor from the opposite category C < sup > op </ sup > to D.

" More immediately, though, he called for a massive build-up of U. S. arms production: " Every realist knows that the democratic way of life is at this moment being ' directly assailed in every part of the world … The need of the moment is that our actions and our policy should be devoted primarily — almost exclusively — to meeting this foreign peril.

More realistically, however, every organization must manage its work, people, processes, technology, etc.

More useful is that every user is drawing on the bandwidth of his or her own news server.

More generally, any collection of events — possibly more than just two of them — are mutually independent if and only if for every finite subset A < sub > 1 </ sub >, ..., A < sub > n </ sub > of the collection we have

More generally, a ( topological ) surface with boundary is a Hausdorff topological space in which every point has an open neighbourhood homeomorphic to some open subset of the upper half-plane H < sup > 2 </ sup >.

This was also the time when every other hero or villain in Spaghetti Westerns started carrying a musical watch, after its ingenious use in For a Few Dollars More.

More than 3, 000 students — three out of every four — take part in at least one for-credit “ service learning ” class by the time that they graduate ; nearly 45 percent participate in a service-learning class in any given year.

One of the characters in the novel compares More favourably to almost every other major historical figure: " He had one completely honest moment right at the end.

More precisely, for every Tychonoff space X, there exists a compact Hausdorff space K such that X is homeomorphic to a subspace of K.

Consequently, “ the decay of population is the greatest evil that a state can suffer ; and the improvement of it the object which ought, in all countries, to be aimed at in preference to every other political purpose whatsoever .” More recently a similar view has been expressed by Smart who argued that all other things being equal a universe with two million happy people is better than a universe with only one million happy people.

More complex situations might involve a program that runs automatically ( say, at 4: 00am every morning ) that similarly requires authentication to get at the data it needs, but there's no human around to log in for them.

More precisely, they showed that there existed positive constants c and C such that for all sufficiently large numbers N, every even number less than N is the sum of two primes, with at most exceptions.

More generally, it is true that every nonzero finitely generated module has a maximal submodule.

More formally, a multivariate random variable is a column vector X = ( X < sub > 1 </ sub >, ..., X < sub > n </ sub >)< sup > T </ sup > ( or its transpose, which is a row vector ) whose components are scalar-valued random variables on the same probability space ( Ω,, P ), where Ω is the sample space, is the sigma-algebra ( the collection of all events ), and P is the probability measure ( a function returning every event's probability ).

More than 6 million cubic feet ( 168, 000 m < sup > 3 </ sup >) of water falls over the crest line every minute in high flow, and almost 4 million cubic feet ( 110, 000 m < sup > 3 </ sup >) on average.

More generally, every topological space which is homeomorphic to an open subset of a complete pseudometric space is a Baire space.

" More precisely, a member of the Jacobson radical must project under the canonical homomorphism to the zero of every " right division ring " ( each non-zero element of which has a right inverse ) internal to the ring in question.

More precisely, Diaconis showed that it takes 5 shuffles before the total variation distance of a 52-card deck begins to drop significantly from the maximum value of 1. 0, and 7 shuffles before it drops below 0. 5 very quickly ( a threshold phenomenon ), after which it is reduced by a factor of 2 every shuffle.

More recently, the publishers have released a new edition about every ten years.

More popular in the 19th and early 20th centuries was the Bolzano – Weierstrass criterion that every sequence admits a convergent subsequence, now called sequential compactness.