This sum becomes larger than any arbitrary real number provided that p is big enough.This shows that there are infinitely many primes, since otherwise this sum would grow only until the biggest prime p is reached.…
The question is now whether this is the same thing as for an arbitrary real number a.If at most one of the two terms in (2) is infinite, then (1) is the same as (2).…
Written language represents the way spoken sounds and words follow one after another by arranging symbols according to a pattern that follows a certain direction.The direction used in a writing system is entirely arbitrary and established by convention.Some writing systems use the horizontal axis (left to right as the Latin script or right to left as the Arabic script), while others such as traditional Chinese writing use the vertical dimension (from top to bottom).…
An individual need not be actually harmed in order to be discriminated against.He or she just needs to be treated worse than others for some arbitrary reason.If someone decides to donate to help orphan children, but decides to donate less, say, to black children out of a racist attitude, he or she will be acting in a discriminatory way even though people he discriminates against are actually benefitted by having some money donated to them.…
However, this cannot be the case for two arbitrary states, although it can hold for certain specific cases.
The natural question arises: at t = 1 is the lamp on or off?There does not seem to be any non-arbitrary way to decide this question.Thomson goes further and claims this is a contradiction.…
We are thus driven to the assumption that the conception is contradictory because incomplete; but how are we to supplement it?What we have must point the way to what we want, or our procedure will be arbitrary.Experience asserts that M is the same (i.e. a mark of the same concept) as N, while logic denies it; and so it being impossible for one and the same M to sustain these contradictory positions there is but one way open to us; we must posit several Ms.…
The letter itself is arbitrary and has no special meaning.Because of the importance of the notion of variable binding and substitution, there is not just one system of lambda calculus, and in particular there are typed and untyped variants.…
Second, he says that, because words are arbitrary, they have meaning only in relation to other words.A dog is a dog because it is not a cat or a mouse or a horse, etc.…
The Physiocrats thought there was a "Natural order" that allowed human beings to live together.Men did not come together via a somewhat arbitrary "social contract".Rather, we have to discover the laws of the natural order that will allow individuals to live in society without losing significant freedoms.…
His strong administration reduced the tyranny of the wealthy over the poor.Yet these good measures were all carried out by arbitrary methods which made them unpopular.Their aim was not the prosperity of the Irish but the benefit to the English exchequer, and Wentworth suppressed the trade in cloth "lest it should be a means to prejudice that staple commodity of England."…
However, the exact procedure of this "authentic tabulation" remained a secret.Some believe song choices were often arbitrary due to various performance and production factors.The show's ad agencies -- initially Lord and Thomas and later Batten, Barton, Durstine & Osborne -- never revealed the specific sources or the methods that were used to determine top hits.…
Much later, the theory of Shimura provided another very explicit class field theory for a class of algebraic number fields.All these very explicit theories cannot be extended to work over arbitrary number field.In positive characteristic p Kawada and Satake used Witt duality to get a very easy description of the p -part of the reciprocity homomorphism.…
The rules are designed so that rarer events require larger drinks.Rule sets for such games are usually arbitrary and local, although they are sometimes published by fan clubs.Matching the characters in the film Withnail and I is such a game.…
The strategy stealing argument assumes that the second player has a winning strategy and demonstrates a winning strategy for the first player.The first player makes an arbitrary move to begin with.After that, he or she pretends that he or she is the second player and adopts the second player's winning strategy.…
This reference state is not always a real state, it may also be a limit, such as with the distances between all bodies tending to infinity, provided that the energy involved in tending to that limit is finite, such as in the case of inverse-square law forces.Any arbitrary reference state could be used, therefore it can be chosen based on convenience.Typically the potential energy of a system depends on the relative positions of its components only, so the reference state can also be expressed in terms of relative positions.…
The "latus rectum" is the chord of the parabola which is parallel to the directrix and passes through the focus.Parabolas can open up, down, left, right, or in some other arbitrary direction.Any parabola can be repositioned and rescaled to fit exactly on any other parabola -- that is, all parabolas are geometrically similar.…
For example; flour, water, yeast, and heat yield bread.The metric of change is arbitrary, so long as the result is generally considered greater.It may be volume, temperature, flavor, efficiency, aesthetic, or whatever.…
Although various official and semi-official appellations were used during the early decades of independent statehood, the title of Prime Minister has been the formal designation of the office at least since 1843.Note that the numbering system in the list is arbitrary and has no official status.The heads of government of the provisional Greek state during the Greek War of Independence, and the subsequent Hellenic State.…
As an illustrative example of how the transformation stack is used, imagine a simple scene with a single model of a person.The person is standing upright, facing an arbitrary direction while his head is turned in another direction.The person is also located at a certain offset from the origin.…
adjectiveBased on or subject to individual discretion or preference or sometimes impulse or caprice →
an arbitrary decision,
the arbitrary rule of a dictator,
an arbitrary penalty,
of arbitrary size and shape,
an arbitrary choice,
arbitrary division of the group into halves