If it were not for an old professor who made me read the classics I would have been stymied on what to do, and now I understand why they are classics ; ;

If I even hint at it do you think it will matter that you are his nephew -- and not even a blood nephew ''??

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

Defoe then commented, `` If they Could Draw that young Gentleman into Their Measures They would show themselves quickly, for they are not asham'd to Say They want only a head to Make a beginning ''.

If Jews are identified as a religious body in a controversy that comes before a national or international tribunal, it is obviously compatible with the goal of human dignity to protect freedom of worship.

If they are right, they will prevail of and by themselves.

Without preliminaries, Esther asked him, `` If you are a world citizen, will you take Garry Davis' place in his tent while he goes to the hospital ''??

If we are to believe the list of titles printed in Malraux's latest book, La Metamorphose Des Dieux, Vol. 1 ( ( 1957 ), he is still engaged in writing a large novel under his original title.

If the would-be joiner asks these questions he is not likely to be duped by extremists who are seeking to capitalize on the confusions and the patriotic apprehensions of Americans in a troubled time.

If we break the minister to our bit, we are buying back our own sins.

If the record buyer's tastes are somewhat eclectic or even the slightest bit esoteric, he will find them satisfied on educational records.

If Daddy's books are out of bounds his own picture books are not.

If it will simply delay the debates until the qualifications are closed next spring, and then carry all the candidates on a tour of debates, it can provide a service to the state.

If they are to be commended for foresight in their planning, what then is the judgment of a town council that compounds this problem during the planning stage??

If the Communists are sincere in wanting a united, neutral and disarmed Germany, it might well be advantageous for the German people in this nuclear age.

If only this could be done more often -- with such heartening results -- many of the earth's `` big problems '' would shrink to the insignificances they really are.

If any are left, presently, we may expect to see signs specifically prohibiting the feeding of them too.

If the raw population figures are crucially relevant, then it is idle to think of liberation, as idle as to suppose that Poland might liberate Russia.

If it is not enough that all of our internationalist One Worlders are advocating that we join this market, I refer you to an article in the New York Times' magazine section ( Nov. 12, 1961 ), by Mr. Eric Johnston, entitled `` We Must Join The Common Market ''.

If the UN troops are not mercenaries then the Hessians were not mercenaries either.

If there is a bounded linear operator from X onto Y, then Y is reflexive.

* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then

If φ is C < sup > k </ sup >, then the inhomogeneous equation is explicitly solvable in any bounded domain D, provided φ is continuous on the closure of D. Indeed, by the Cauchy integral formula,

If X is a set and M is a complete metric space, then the set B ( X, M ) of all bounded functions ƒ from X to M is a complete metric space.

If X is a topological space and M is a complete metric space, then the set C < sub > b </ sub >( X, M ) consisting of all continuous bounded functions ƒ from X to M is a closed subspace of B ( X, M ) and hence also complete.

If the length of the line is bounded, customers are being " processed " and output as rapidly, on average, as they are being inputted and that process is real-time.

In analysis the infimum or greatest lower bound of a subset S of real numbers is denoted by inf ( S ) and is defined to be the biggest real number that is smaller than or equal to every number in S. If no such number exists ( because S is not bounded below ), then we define inf ( S ) = −∞.

If the matrix is positive semidefinite matrix, then is a convex function: In this case the quadratic program has a global minimizer if there exists some feasible vector ( satisfying the constraints ) and if is bounded below on the feasible region.

If supply expands from S < sub > 0 </ sub > to S < sub > 1 </ sub >, the consumers ' surplus expands to the triangle above P < sub > 1 </ sub > and below the demand line ( still bounded by the price axis ).

* Suppose that is a sequence of Lipschitz continuous mappings between two metric spaces, and that all have Lipschitz constant bounded by some K. If ƒ < sub > n </ sub > converges to a mapping ƒ uniformly, then ƒ is also Lipschitz, with Lipschitz constant bounded by the same K. In particular, this implies that the set of real-valued functions on a compact metric space with a particular bound for the Lipschitz constant is a closed and convex subset of the Banach space of continuous functions.

* If is a polynomial, then is the boundary of the filled Julia set ; that is, those points whose orbits under iterations of remain bounded.

If a set is compact, then it is bounded.

If is a closed bounded interval, we also allow the possibility ( this convention makes it possible to talk about " closed " simple curves, see below ).

If the universe is bounded, this does not imply anything about the sign of its curvature.

If approved, the area bounded by Auburn Boulevard on the north, the American River Drive, Ethan Way on the west, and Mission Avenue / Jacob Lane on the east would have become the City of Arden-Arcade.

If is a monotone sequence of real numbers ( i. e., if a < sub > n </ sub > ≤ a < sub > n + 1 </ sub > or a < sub > n </ sub > ≥ a < sub > n + 1 </ sub > for every n ≥ 1 ), then this sequence has a finite limit if and only if the sequence is bounded.

: If it is known that a group G with m generators and exponent n is finite, can one conclude that the order of G is bounded by some constant depending only on m and n?

If is a smooth well-behaved function, integrated over a small number of dimensions and the limits of integration are bounded, there are many methods of approximating the integral with arbitrary precision.

If a formula is logically equivalent to a formula with only bounded quantifiers then is assigned the classifications and.

Given the representation of T as a multiplication operator, it is easy to characterize the Borel functional calculus: If h is a bounded real-valued Borel function on R, then h ( T ) is the operator of multiplication by the composition.

: If and are normal operators and if A is a bounded linear operator such that, then.

# If M is a complete Riemannian manifold with sectional curvature bounded above by a strictly negative constant k then it is a CAT ( k ) space.

If T is a closed operator ( which includes the case that T is a bounded operator ), boundedness of such inverses follow automatically if the inverse exists at all.

If λI − T is invertible then that inverse is linear ( this follows immediately from the linearity of λI − T ), and by the bounded inverse theorem is bounded.