In practice, the existence of a continuous extension of the difference quotient Q ( h ) to is shown by modifying the numerator to cancel h in the denominator.

The actions Q took in sending the Enterprise D to System J-25 — and thus maintaining the time loop, are expanded upon in the Star Trek novels as being partially ( though indirectly ) the reason for the existence of the Mirror Universe, explaining that Zefram Cochrane attempted to warn Earth and the worlds that would become part of the Federation about the Borg after First Contact.

* Q Continuum, a parallel existence in the fictional Star Trek universe where omnipotent entities all known as Qs exist

Since its discovery, many scholars see it as evidence in support of the existence of the so-called Q source, which might have been very similar in its form as a collection of sayings of Jesus without any accounts of his deeds or his life and death, a so-called " sayings gospel ".

The 2SH attempts to solve the synoptic problem by advancing two propositions, Markan priority to explain the triple tradition, and the existence of a lost Q document to solve the double tradition.

The 2SH explains the double tradition by postulating the existence of a lost " sayings of Jesus " document known as Q, from the German Quelle, " source ".

While the 2SH remains the most popular explanation for the origins of the synoptic gospels, two questions, the existence of the so-called " minor agreements ", and problems with the hypothesis of Q, continue at the centre of discussion over its explanatory power.

" Therefore, the minor agreements, if taken seriously, force a choice between accepting pure Markan priority on one hand or the existence of Q on the other hand, but not both simultaneously as the 2SH requires.

A principal objection to the 2SH is that it requires a hypothetical document, Q, the existence of which is not attested in any way, either by existing fragments ( and a great many fragments of early Christian documents do exist ) or by early Church tradition.

Another fundamental feature of modern Bible studies is the presumption of the existence of Q, a written source, now lost, hypothesized to have been used both by Matthew and by Luke.

The 2SH explains the double tradition by postulating the existence of a lost " sayings of Jesus " document known as Q.

The elements of the quotient group R / Q partition R. There are uncountably many elements, and each element is dense in R. Each element of R / Q intersects 1, and the axiom of choice guarantees the existence of a subset of 1 containing exactly one representative out of each element of R / Q.

The quinque viae ( Latin: five ways ) found in the Summa Theologica ( I, Q. 2, art. 3 ) are five arguments demonstrating the existence of God, which today are categorized as:

A categorical proposition contains a subject and predicate where the existential impact of the copula implies the proposition as referring to a class with at least one member, in contrast to the conditional form of hypothetical or materially implicative propositions, which are compounds of other propositions, e. g. If P, then Q, where P and Q are both propositions, and their existential impact is dependent upon further propositions where in quantification existence is instantiated ( existential instantiation ).

The form of the Gospel of Thomas was often argued to corroborate the existence of the Q Gospel, whose hypothetical form would resemble it.

Finally, William Riker of the USS Enterprise denies any claim to have known Quinn at all, until Q shows Riker that Quinn had helped his family in the past: As a soldier in the American Civil War, Quinn carried a wounded Union officer, Colonel Thaddeus Riker, back from the front lines to safety-ultimately ensuring Will Riker's existence in the future.

The APD / MD for Q 104. 3's entire existence as a hard rock station was Vinny Marino.

Q is interpretable in a fragment of Zermelo's axiomatic set theory, consisting of extensionality, existence of the empty set, and the axiom of adjunction.

Farmer argued that a modification of the Augustinian hypothesis, ordering Matthew-Luke-Mark, eliminated all reasons for the existence of Q, a position whose credibility was conceded by W. C. Allen and others.

A sufficiently powerful entity in such a world would have the capacity to travel backwards in time to a point before its own existence, and to then create itself, thereby initiating everything which follows from it.

Rosser 1939 addresses the notion of " effective computability " as follows: " Clearly the existence of CC and RC ( Church's and Rosser's proofs ) presupposes a precise definition of " effective ".

Since any Godlike object is necessarily existent, it follows that any Godlike object in one world is a Godlike object in all worlds, by the definition of necessary existence.

It is deduced from the model existence theorem as follows: if there is no formal proof of a formula then adding its negation to the axioms gives a consisten theory, which has thus a model, so that the formula is not a semantic consequence of the initial theory.

To do this, we take for granted that is meromorphic in the half-plane, and is analytic there except for a simple pole at, and that there is a product formula for This product formula follows from the existence of unique prime factorization of integers, and shows that is never zero in this region, so that its logarithm is defined there and Write ; then

As many more individuals of each species are born than can possibly survive ; and as, consequently, there is a frequently recurring struggle for existence, it follows that any being, if it vary however slightly in any manner profitable to itself, under the complex and sometimes varying conditions of life, will have a better chance of surviving, and thus be naturally selected.

In the sociology of Émile Durkheim, sui generis is used to illustrate his theory of an independence in social existence, as follows.

Clause 3. provided as follows :- Independent Arab and Jewish States and the Special International Regime for the City of Jerusalem, set forth in part III of this plan, shall come into existence in Palestine two months after the evacuation of the armed forces of the mandatory Power has been completed but in any case not later than 1 October 1948.

Sommer ( 2008 ) classified historical accounts related to vitamin A and / or manifestations of deficiency as follows: " Ancient " accounts ; 18th-to 19th-century clinical descriptions ( and their purported etiologic associations ); early 20th-century laboratory animal experiments, and clinical and epidiomologic observations that identified the existence of this unique nutrient and manifestations of its deficiency.

It follows from the existence theorem for limits that a category is complete if and only if it has equalizers ( of all pairs of morphisms ) and all ( small ) products.

The argument that corruption necessarily follows from the opportunity is weakened by the existence of countries with low to non-existent corruption but large public sectors, like the Nordic countries.

U. S. 9 exits shortly after the bridge to go onto New York City's Broadway north of it, passing over the northern tip of Manhattan Island via the toll-free Broadway Bridge, through the Bronx and into Westchester County, where in some towns it follows the old Albany Post Road, which dates from the early days of the nation's existence.

The existence of is probably an accident, as it follows a pattern of PUSH and POP instruction opcodes for the four segment registers on the 8086 and 8088 .</ ref >).

However, if R is the ring of algebraic integers in an algebraic number field, or more generally a Dedekind domain, the multiplication defined above turns the set of fractional ideal classes into an abelian group, the ideal class group of R. The group property of existence of inverse elements follows easily from the fact that, in a Dedekind domain, every non-zero ideal ( except R ) is a product of prime ideals.

The existence of many noncomputable sets follows from the facts that there are only countably many Turing machines, and thus only countably many computable sets, but there are uncountably many sets of natural numbers.

Al-Jahiz's ideas on the struggle for existence in the Book of Animals have been summarized as follows:

His argument for the subsistence and incorruptibility of the intellectual soul takes its point of departure from the metaphysical principle that operation follows upon being ( agiture sequitur esse ), i. e., the activity of a thing reveals the mode of being and existence it depends upon.

However, boundedness of the inverse does follow directly from its existence if one introduces the additional assumption that T is closed ; this follows from the closed graph theorem.

The elements of a valid cause of action for abuse of process in most common law jurisdictions are as follows: ( 1 ) the existence of an ulterior purpose or motive underlying the use of process, and ( 2 ) some act in the use of the legal process not proper in the regular prosecution of the proceedings.

The first part of this paper takes the form of a reply to an argument for the existence of Universals: from observing that we do use words such as " grey " or " circular " and that we use a single term in each case, it follows that there must be a something that is named by such terms — a universal.

Its existence is unprovable in ZFC, the standard form of axiomatic set theory, but follows from a suitable large cardinal axiom.

It follows from Jensen's covering theorem that the existence of 0 < sup >#</ sup > is equivalent to ω < sub > ω </ sub > being a regular cardinal in the constructible universe L.

It follows that the existence of 0 < sup >#</ sup > contradicts the axiom of constructibility: V = L.

It follows that past and future pleasure have no real existence for us, and that among present pleasures there is no distinction of kind.