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Page "Modulus of continuity" ¶ 19
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If and are
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 and functions
If Af denotes the space of N times continuously differentiable functions, then the space V of solutions of this differential equation is a subspace of Af.
If we are discussing differentiable complex-valued functions, then Af and V are complex vector spaces, and Af may be any complex numbers.
If the inner functions of religion are performed, the individual is a composed, ordered, motivated, and emotionally secure associate ; ;
* If M is some set and S denotes the set of all functions from M to M, then the operation of functional composition on S is associative:
Theorem: If K < sub > 1 </ sub > and K < sub > 2 </ sub > are the complexity functions relative to description languages L < sub > 1 </ sub > and L < sub > 2 </ sub >, then there is a constant c – which depends only on the languages L < sub > 1 </ sub > and L < sub > 2 </ sub > chosen – such that
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 G is a locally compact Hausdorff topological group and μ its Haar measure, then the Banach space L < sup > 1 </ sup >( G ) of all μ-integrable functions on G becomes a Banach algebra under the convolution xy ( g ) = ∫ x ( h ) y ( h < sup >− 1 </ sup > g ) dμ ( h ) for x, y in L < sup > 1 </ sup >( G ).
If x is held fixed, then the Bessel functions are entire functions of α.
If one axiomatizes relations instead of functions, one obtains the theory of allegories.
If we take the simple molecular orbital description of the ground state and combine that function with the functions describing all possible excited states using unoccupied orbitals arising from the same set of atomic orbitals, we also reach the full configuration interaction wavefunction.
If F is clear from context then Ω < sub > F </ sub > may be denoted simply Ω, although different prefix-free universal computable functions lead to different values of Ω.
If ( 1a ) and ( 1b ) hold for a differentiable pair of functions u and v, then so do
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 one identifies C with R < sup > 2 </ sup >, then the holomorphic functions coincide with those functions of two real variables with continuous first derivatives which solve the Cauchy-Riemann equations, a set of two partial differential equations.
If a hellbender ends up in an area of slowly moving water, not enough water will pass over its skin in a given time period, making it difficult to garner enough oxygen to support necessary respiratory functions.
If we think of composition as a kind of multiplication of functions, this identity says that the inverse of a function is analogous to a multiplicative inverse.
If the Board recommends approval, and the General Conference approves the application for membership, the State must then submit its instrument of acceptance of the IAEA Statute to the United States, which functions as the depositary Government for the IAEA Statute.
* If the molecule has some symmetry, the degenerate atomic orbitals ( with the same atomic energy ) are grouped in linear combinations ( called symmetry-adapted atomic orbitals ( SO )), which belong to the representation of the symmetry group, so the wave functions that describe the group are known as symmetry-adapted linear combinations ( SALC ).
If motivation does not take place in an organization, then employees may not contribute to the other functions ( which are usually set by top-level management ).
If f and g are two multiplicative functions, one defines a new multiplicative function f * g, the Dirichlet convolution of f and g, by

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