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 the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If he is good, he may not be legal ; ;

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If the existent form is to be retained new factors that reinforce it must be introduced into the situation.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.

If he is a traditionalist, he is an eclectic traditionalist.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

If he found data that fitted his general plan, he used it and counted his sources trustworthy.

If they are used, the walls and roof should be 10 inches thick to give the same protection as the 8-inch solid concrete blocks.

If your state has no provisions for the numbering of pleasure boats, you must apply for a number from the U.S. Coast Guard for any kind of boat with mechanical propulsion rated at more than 10 horsepower before it can be used on Federal waterways.

Note: If 1/2-inch panel board is used inside and out, or 5/8-inch one side and 3/8-inch the other, and 1/8-inch glass is used, stock lumber in Af, Af, and Af can be used in making the glass panels.

If only state funds were used to pay for the vocational education, it could be argued that the state should not have to bear the cost of vocational training which would benefit employers in other states.

If the master of scops who was most responsible for the poem ever used kennings that were traditional, he was at least partly deprived of free will and not inclined towards shrewd and sophisticated misuse of speech elements.

If the one- or two-digit address of an index word or electronic switch is used or is included in the operand of an XRESERVE or SRESERVE statement ( see page 99 ), the corresponding index word or electronic switch is reserved.

If the voice is just a shade less glorious than it used to be, it is still a beautiful instrument, controlled and flexible.

If, for instance, someone says " I buried $ 100 in the bank ", most people would not think someone used a shovel to dig in the mud.

If " biweekly " is used in a conversation about a meeting schedule, it may be difficult to infer which meaning was intended.

If the Greek letter is used, it is assumed to be a Fourier transform of another function,

If the latter, Amaryllis would be the correct name for the genus Hippeastrum, and a different name would have to be used for the genus discussed here.

If an alpha channel is used in an image, it is common to also multiply the color by the alpha value, to save on additional multiplications during compositing.

If this article / noun pair is used as the object of a verb, it ( usually ) changes to the accusative case, which entails an article shift in German – Ich sehe den Wagen.

If, conversely, tin is used to coat steel, when a breach of the coating occurs it actually accelerates oxidation of the iron.

If the amount in the sample is below an instrument's range of measurement, the method of addition can be used.

If an ESN / MIN Pair is intercepted, it could then be cloned onto a different phone and used in other areas for making calls without paying.

If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

If used for drinking, mineral supplements or mineralization is necessary.

If the assets used are not identical ( so a price divergence makes the trade temporarily lose money ), or the margin treatment is not identical, and the trader is accordingly required to post margin ( faces a margin call ), the trader may run out of capital ( if they run out of cash and cannot borrow more ) and go bankrupt even though the trades may be expected to ultimately make money.

If chosen, the SysOp could then initiate a text-to-text chat with the caller ; similar to what commercial websites have used to sell and support products.

If either one die or the other but not both can be moved, the higher must be used.

If F. tularensis were used as a weapon, the bacteria would likely be made airborne for exposure by inhalation.