If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.

If Bultmann's own definition of myth is strictly adhered to ( and it is interesting that this is almost never done by those who make such pronouncements ), the evidence is overwhelming that he does not at all exaggerate the extent to which the mythological concepts of traditional theology have become incredible and irrelevant.

If we define tangent covectors in terms of equivalence classes of smooth maps vanishing at a point then the definition of the pullback is even more straightforward.

If we consider the thesis and its converse as definition, then the hypothesis is an hypothesis about the application of the mathematical theory developed from the definition.

If one employs the strict, limited definition of crannog which requires the use of timber, then sites in the Western Isles are stricken from the discussion.

If the XML document type declaration includes any SYSTEM identifier for the external subset, it can't be safely processed as standalone: the URI should be retrieved, otherwise there may be unknown named character entities whose definition may be needed to correctly parse the effective XML syntax in the internal subset or in the document body ( the XML syntax parsing is normally performed after the substitution of all named entities, excluding the five entities that are predefined in XML and that are implicitly substituted after parsing the XML document into lexical tokens ).

If one concept is defined by another, and the other is defined by the first, this is known as circular definition, somewhat similar to a circular reasoning: neither offers us any enlightenment about what we wanted to know.

If ' beauty ' is defined as ' aesthetically successful ', one must continue to break down and define the following definition.

If confirmed, this would imply special relativity is an approximation to a more general theory, but since the relevant comparison would ( by definition ) be outside the observable universe, it is difficult to imagine ( much less construct ) experiments to test this hypothesis.

If R is an integral domain then any two gcd's of a and b must be associate elements, since by definition either one must divide the other ; indeed if a gcd exists, any one of its associates is a gcd as well.

If the term has nonetheless retained a certain consistency in its use across these fields and would-be movements, it perhaps reflects the word ’ s position in general English usage: though the standard dictionary definition of irreal gives it the same meaning as unreal, irreal is very rarely used in comparison with unreal.

If the particles are indistinguishable, this is impossible by definition ; either particle can be in either state.

In 2001, David Wiley criticized learning object theory in his paper, The Reusability Paradox which is summarized by D ' Arcy Norman as, If a learning object is useful in a particular context, by definition it is not reusable in a different context.

Most states followed the federal definition of interrogation Innis rule If “ Yes ” go to 2 ; If “ No ”, Miranda does not apply.

If only the second and third conditions of the definition of measure above are met, and takes on at most one of the values, then is called a signed measure.

Proof: If there is no possible move, then the lemma is vacuously true ( and the first player loses the normal play game by definition ).

If a great number of attributes end up being the same as on the definition, a great amount of information can be " inherited ", and not have to be redundantly specified in the netlist, saving space, and making the design easier to read by both machines and people.

If the future was given the definition of Physics, it can be drawn down to this.

If ( x, y ) is a point on the parabola then, by Pappus ' definition of a parabola, it is the same distance from the directrix as the focus ; in other words:

The algorithm for deciding this is conceptually simple: it constructs ( the description of ) a new program t taking an argument n which ( 1 ) first executes program a on input i ( both a and i being hard-coded into the definition of t ), and ( 2 ) then returns the square of n. If a ( i ) runs forever, then t will never get to step ( 2 ), regardless of n. Then clearly, t is a function for computing squares if and only if step ( 1 ) terminates.

He also has a simple definition for talent in writing: " If you wrote something for which someone sent you a check, if you cashed the check and it didn't bounce, and if you then paid the light bill with the money, I consider you talented.

If the center is a distinguished point considered as origin of E, as in a normed space, it is not mentioned in the definition and notation.

If the average speed and time of travel is known, distance traveled can be found by a rearrangement of the definition, leaving us with:

If you would feel happier with full collision insurance, there is a small additional charge, again varying from country to country and depending on the term of such insurance.

If F ( r ) represents gravity, it is a negative term proportional to 1 / r < sup > 2 </ sup >, so the net acceleration in r in the rotating frame depends on a difference of reciprocal square and reciprocal cube terms, which are in balance in a circular orbit but otherwise typically not.

If this acceleration is multiplied by the particle mass, the leading term is the centripetal force and the negative of the second term related to angular acceleration is sometimes called the Euler force.

If every term of every definiens must itself be defined, " where at last should we stop?

He is still seeking greater autonomy from China, although Dolma Gyari, deputy speaker of the parliament-in-exile has stated " If the middle path fails in the short term, we will be forced to opt for complete independence or selfdetermination as per the UN charter ".

If the source of Φ ( r ) is a dipole, as it is assumed here, this term is the only non-vanishing term in the multipole expansion of Φ ( r ).

If f is a polynomial and p is big enough, then the remainder term vanishes.

If is a quaternion valued spinor, is quaternion hermitian 4x4 matrix coming from Sp ( 8 ) and is a pure imaginary quaternion ( both of which are 4-vector bosons ) then the interaction term is:

If Good Times was not stopped in time, an infected computer would enter an " nth-complexity infinite binary loop " ( a meaningless term ), damaging the processor.

If less than two years after his election, Somoza Garcia, defying the Conservative Party, declared his intention to stay in power beyond his presidential term.

If we shift the constant term to the right hand side, factor a p and multiply by q < sup > n </ sup >, we get

If we instead shift the leading term to the right hand side and multiply by q < sup > n </ sup >, we get

If the equation lacks a constant term a < sub > 0 </ sub >, then 0 is one of the rational roots of the equation.

If a term such as ' plosive ' is used for oral obstruents, and nasals are not called nasal stops, then a stop may then mean the glottal stop ; ' plosive ' may even mean non-glottal stop.

If immediate treatment is successful, the patient may improve ( although this may be temporary ) and this improvement may allow the patient to be categorized to a lower priority in the short term.

If a senator died, resigned, or was expelled, the legislature of the state would appoint a replacement to serve out the remainder of the senator's term.

Here the notion of causality is one of contributory causality as discussed above: If the true value, then a change in will result in a change in y unless some other causative variable ( s ), either included in the regression or implicit in the error term, change in such a way as to exactly offset its effect ; thus a change in is not sufficient to change y.

If a political offense was not the official reason for detention, the term would imply that the detention was motivated by the prisoner's politics.

If there is no break in activity, this is considered a tornado outbreak ( although the term " tornado outbreak " has various definitions ).

If they do not, then the term Marginata is used, but sometimes these terms are used simultaneously.

If standard quantifier rules are used, however, every term must refer to something that exists in all the possible worlds.

If the government was any sort of federal democracy, there is no evidence of it, as the term " dynastic " suggests.