If F ≥ F < sub > Critical </ sub > ( Numerator DF, Denominator DF, α )

If x is held fixed, then the Bessel functions are entire functions of α.

If α is an integer, the limit has to be calculated.

* Scanning: If a is the next symbol in the input stream, for every state in S ( k ) of the form ( X → α • a β, j ), add ( X → α a • β, j ) to S ( k + 1 ).

If one chooses a critical value of the test statistic D < sub > α </ sub > such that P ( D < sub > n </ sub > > D < sub > α </ sub >)

If A is a directed set, we often write a net from A to X in the form ( x < sub > α </ sub >), which expresses the fact that the element α in A is mapped to the element x < sub > α </ sub > in X.

If ( x < sub > α </ sub >) is a net from a directed set A into X, and if Y is a subset of X, then we say that ( x < sub > α </ sub >) is eventually in Y ( or residually in Y ) if there exists an α in A so that for every β in A with β ≥ α, the point x < sub > β </ sub > lies in Y.

If ( x < sub > α </ sub >) is a net in the topological space X, and x is an element of X, we say that the net converges towards x or has limit x and write

If c, h, and e were all changed so that the values they have in metric ( or any other ) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our World.

If α were > 0. 1, stellar fusion would be impossible and no place in the universe would be warm enough for life as we know it.

If I is an index set and X < sub > I </ sub > is the set of indeterminates X < sub > i </ sub > for i ∈ I, then a monomial X < sup > α </ sup > is any finite product of elements of X < sub > I </ sub > ( repetitions allowed ); a formal power series in X < sub > I </ sub > with coefficients in a ring R is determined by any mapping from the set of monomials X < sup > α </ sup > to a corresponding coefficient c < sub > α </ sub >, and is denoted.

If we consider a cell of the " net ", we can see that the cell is a rhombus: it is a parallelogram with the four sides equal to d = p / sin α ; ( we have a right triangle which hypothenuse is d and the side opposed to the α angle is p ).

If f is assumed to be continuous as well then this can be extended to show that homogeneity for α any real number, using the fact that rationals form a dense subset of the reals.

* If α is an algebraic integer then is another algebraic integer.

If a test of significance gives a p-value lower than the significance level α, the null hypothesis is rejected.

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 the media agency responsible for the authorized production allows material from fans, what is the limit before legal constraints from actors, music, and other considerations, come into play?

If this limit doesn't exist then there is no oblique asymptote in that direction.

If this limit fails to exist then there is no oblique asymptote in that direction, even should the limit defining m exist.

If a main-sequence star is not too massive ( less than approximately 8 solar masses ), it will eventually shed enough mass to form a white dwarf having mass below the Chandrasekhar limit, which will consist of the former core of the star.

If this limit exists, then it may be computed by taking the limit as h → 0 along the real axis or imaginary axis ; in either case it should give the same result.

This is a Cauchy sequence of rational numbers, but it does not converge towards any rational limit: If the sequence did have a limit x, then necessarily x < sup > 2 </ sup > = 2, yet no rational number has this property.

If the limit exists, then f is differentiable at a.

If the limit exists, meaning that there is a way of choosing a value for Q ( 0 ) that makes the graph of Q a continuous function, then the function f is differentiable at a, and its derivative at a equals Q ( 0 ).

If it can be claimed that it is ethical to limit the internet and other technology to only users who have the means to utilize these software, then there is no argument against the way things are at the moment ; there is no need to complain if all morality is in affect.

Given a trigonometric series f ( x ) with S as its set of zeros, Cantor had discovered a procedure that produced another trigonometric series that had S ' as its set of zeros, where S ' is the set of limit points of S. If p ( 1 ) is the set of limit points of S, then he could construct a trigonometric series whose zeros are p ( 1 ).

If and then the limit is where is the complete elliptic integral of the first kind

If the limit exists, we say that ƒ is complex-differentiable at the point z < sub > 0 </ sub >.

This can be verified simply by investigating, e. g., a polycrystalline material under a polarizing microscope having the polarizers crossed: If the crystallites are larger than the resolution limit, they will be visible.

If it does, however, it is unique in a strong sense: given any other inverse limit X ′ there exists a unique isomorphism X ′ → X commuting with the projection maps.

If a claims adjuster suspects under-insurance, the condition of average may come into play to limit the insurance company's exposure.

If the time limit is reached and only one competitor has a point, that competitor wins.

If the brightness of the object exceeded the maximum limit of eight times the brightness of Canopus, the spacecraft would search for a new star.

If the offer is for a longer period courts will limit the offer period to 90 days.

If a criminal is on the run, he can be convicted in absence, in order to prevent prescription, or the time limit does not elapse during that time.