If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.

If interstellar colonization is possible, then this assumption is invalid, and the equations of population dynamics would apply instead.

If the wavepacket has a relatively large frequency spread, or if the dispersion has sharp variations ( such as due to a resonance ), or if the packet travels over very long distances, this assumption is not valid.

If the Zubrin / Andrews assumption were correct then d / dt ( mv < sub > 1 </ sub >) =

If we use NC reductions, that is, reductions which can operate in polylogarithmic time on a parallel computer with a polynomial number of processors, then all P-complete problems lie outside NC and so cannot be effectively parallelized, under the unproven assumption that NC ≠ P. If we use the weaker log-space reduction, this remains true, but additionally we learn that all P-complete problems lie outside L under the weaker unproven assumption that L ≠ P. In this latter case the set P-complete may be smaller.

If the computational Diffie – Hellman assumption holds in the underlying cyclic group, then the encryption function is one-way.

If the decisional Diffie – Hellman assumption ( DDH ) holds in, then

If instead of assuming a constant rate of usage, the assumption of a constant rate of growth of annually is made, the resource will instead last

If, however, there are some extreme events taken from thunder storms, others from snow pack melting, and others from hurricanes, then this assumption is most likely not valid.

If words and expressions that imply that women or men are inferior are constantly used, that assumption of inferiority tends to become part of our mindset ….

If one is dealing with continuous data, a typical assumption is that the continuous values associated with each class are distributed according to a Gaussian distribution.

If there were not, then the entire graph would be the union of finitely many finite sets, and thus finite, contradicting the assumption that the graph is infinite.

If that the justification of induction cannot be deductive, then it would beg the question for induction to be based on an inductive assumption about a connection.

" If they wish to assert their claim to Trans-Jordan and to avoid raising with other Powers the legal status of that area, they can only do so by proceeding upon the assumption that Trans-Jordan forms part of the area covered by the Palestine Mandate.

... it is incorrect to speak of an assumption as either true or false, since there is no way of proving it to be either ( If there were, it would no longer be an assumption ).

If such a dichotomy theorem is true, then CSPs provide one of the largest known subsets of NP which avoids NP-intermediate problems, whose existence was demonstrated by Ladner's theorem under the assumption that P ≠ NP.

If they share an assumption, belief or understanding of how the contract will be interpreted or what the legal effect will be, they are bound by that belief, assumption or understanding if:

If I ’ m persuaded that our life is predicated upon violence, that the entire structure of what we call civilization, the scaffolding that we ’ ve built up over the millennia, can collapse at any moment, then whatever I write is going to be affected by that assumption.

This most usually implicit assumption must be stated explicitly, otherwise the definition is incorrect: If water is added to a pot containing salty water, the concentration of salt decreases, although there is no chemical reaction.

If Russian pupils have to take these languages, how come American students have a choice whether or not to take a language, but have to face so many exceptions??

If the Czech ethnic origin was to be stressed, combinations like " Bohemian of Bohemian language "( Čech českého jazyka ), " a real Bohemian " ( pravý Čech ) etc.

If names be not correct, language is not in accordance with the truth of things.

If language be not in accordance with the truth of things, affairs cannot be carried on to success.

If the possibility of adding the empty string to a language is added to the strings recognized by the noncontracting grammars ( which can never include the empty string ) then the languages in these two definitions are identical.

If these two features of the language coincide too frequently, they overemphasize each other and the hexameter becomes sing-songy.

If Solomon was the author, the book underwent a later modernization of language.

If this is the case, the non-Pauline language and style are not indications of pseudonymity.

If someone sees something completely different than another, our language prevents us from acknowledging the other's point of view by limiting our perception to fixed states.

* If the entire language does not allow side-effects, then any evaluation strategy can be used ; this gives the compiler freedom to reorder or combine the evaluation of expressions in a program ( for example, using deforestation ).

If Language A borrowed a word from Language B, or both borrowed the word from a third language or inherited it from a common ancestor, and later the word shifted in meaning or acquired additional meanings in at least one of these languages, a native speaker of one language will face a false friend when learning the other.

If the facts are related, this would be a unique case of a tradition that endured for more than a thousand years and that actually pre-dates most of the major splits in the Germanic language family.

# If the borrowed word happens to have a suffix that the borrowing language uses as a gender marker, the suffix tends to dictate gender.

If V is a formal language, then V < sub > i </ sub >, the i-th power of the set V, is a shorthand for the concatenation of set V with itself i times.

If negation is cyclic and "∨" is a " max operator ", then the law can be expressed in the object language by ( P ∨ ~ P ∨ ~~ P ∨ ... ∨ ~...~ P ), where "~...~" represents n − 1 negation signs and "∨ ... ∨" n − 1 disjunction signs.

If such a language existed, Zamenhof postulated, it could play the role of a neutral communication tool between people of different ethnic and linguistic backgrounds.

If something was already there with no conflict, he used it without changes in language, he reordered and ruled on where there was conflict, and clarified where context was not given.

If a model for a language moreover satisfies a particular sentence or theory ( set of sentences satisfying special conditions ), it is called a model of the sentence or theory.

If they express much more than this, they are usually considered to be a hardware description language such as Verilog, VHDL, or any one of several specific languages designed for input to simulators.

If a language uses multiple writing systems, it may have distinct orthographies, as is the case with Kurdish, Uyghur, Serbian, Inuktitut and Turkish.

It is this emphasis on becoming attentive to the social backdrop against which language is rendered intelligible that explains Wittgenstein's elliptical comment that " If a lion could talk, we could not understand him.

Many of his stories, such as Gulf, If This Goes On —, and Stranger in a Strange Land, depend strongly on the premise, related to the well-known Sapir – Whorf hypothesis, that by using a correctly designed language, one can change or improve oneself mentally, or even realize untapped potential ( as in the case of Joe Green in Gulf ).

Klement returned his bicycle to the manufacturers, Seidel and Naumann, with a letter, in Czech, asking them to carry out repairs, only to receive a reply, in German, stating: " If you would like an answer to your inquiry, you should try writing in a language we can understand ".