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If and third
If we examine the three types of change from the point of view of their internal structure we find an additional profound difference between the third and the first two, one that accounts for the notable difference between the responses they evoke.
If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.
If there was realism in the theater, there would never be a third act.
* If the third baseman fields a ball and throws it to first, it is recorded as a 5 – 3 out.
If a Committee manages to adopt a joint text, it then has to be approved in a third reading by both the Council and Parliament or the proposal is abandoned.
If the ideals A and B of R are coprime, then AB = A ∩ B ; furthermore, if C is a third ideal such that A contains BC, then A contains C. The Chinese remainder theorem is an important statement about coprime ideals.
In particular, the third anathema reads: " If anyone divides in the one Christ the hypostases after the union, joining them only by a conjunction of dignity or authority or power, and not rather by a coming together in a union by nature, let him be anathema.
If a team fails to gain ten yards in two downs they usually punt the ball on third down or try to kick a field goal ( see below ), depending on their position on the field.
If objects are seen as moving within a rotating frame, this movement results in another fictitious force, the Coriolis force ; and if the rate of rotation of the frame is changing, a third fictitious force, the Euler force is experienced.
If the third layer is placed so that its atoms are directly above those of the first layer, the stacking will be ABA — this is the hcp structure, and it continues ABABABAB.
If the panegyric detailing the ceremony implied that the true center of the Empire was not Rome, but where the Emperor sat ("... the capital of the Empire appeared to be there, where the two emperors met "), it simply echoed what had already been stated by the historian Herodian in the early third century: " Rome is where the emperor is ".
If his son were guilty, he would still believe him innocent, on the basis of faith in his son ; this would violate the third subjunctive condition.
The parallel postulate: If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.
If there is another functional group at a carbon, it may be named with the Greek letter, e. g., the gamma-amine in gamma-aminobutanoic acid is on the third carbon of the carbon chain attached to the carboxylic acid group.
If the team that batted second is substantially behind on first innings total, it may be required to bat again ( i. e., to immediately follow on from its first innings ) in the third innings of the match.
If anyone violates the truce of God and after the third admonition does not make satisfaction, he shall be anathematized.
If he disregards the third admonition the bishop, either with the advice of the metropolitan or with that of two or one of the neighboring bishops, shall pronounce the sentence of anathema against the violator and in writing denounce him to all the bishops.
If the Supreme Court grants certiorari and accepts the case, it will receive written briefs from each side ( and any amici curiae or friends of the court — usually interested third parties with some expertise to bear on the subject ) and schedule oral arguments.
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 you listened very carefully, I have already stated to you what the third word is.
If you have read what I have told you, you will see that I have given you the third word.
If one carefully observes the third equation one will notice it also works for n
If the monopoly were permitted to charge individualised prices ( this is termed third degree price discrimination ), the quantity produced, and the price charged to the marginal customer, would be identical to that of a competitive company, thus eliminating the deadweight loss ; however, all gains from trade ( social welfare ) would accrue to the monopolist and none to the consumer.
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.

If and identity
If Arthur Williams was involved in the fraud or the murder, then he too had another identity.
If the replica had all the same experiences, traits, and physical appearances of the first person, we would all attribute the same identity to the second, according to Hick.
If the norm of a Banach space satisfies this identity, the associated inner product which makes it into a Hilbert space is given by the polarization identity.
If X is a real Banach space, then the polarization identity is
If a pope dies before revealing the identity of an in pectore cardinal, the cardinalate expires.
Linear Diophantine equations take the form ax + by = c. If c is the greatest common divisor of a and b then this is Bézout's identity, and the equation has an infinite number of solutions.
If G = GL < sub >*</ sub >( K ), then the set of natural numbers is a proper subset of G < sub > 0 </ sub >, since for each natural number n, there is a corresponding identity matrix of dimension n. G ( m, n ) is empty unless m = n, in which case it is the set of all nxn invertible matrices.
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.
Then an element e of S is called a left identity if e * a = a for all a in S, and a right identity if a * e = a for all a in S. If e is both a left identity and a right identity, then it is called a two-sided identity, or simply an identity.
* If a is idempotent in the ring R, then aRa is again a ring, with multiplicative identity a.
If a is a central idempotent, then the corner ring is a ring with multiplicative identity a.
If R is the direct sum of the rings R < sub > 1 </ sub >,..., R < sub > n </ sub >, then the identity elements of the rings R < sub > i </ sub > are central idempotents in R, pairwise orthogonal, and their sum is 1.
If a is an idempotent of the endomorphism ring End < sub > R </ sub >( M ), then the endomorphism is an R module involution of M. That is, f is an R homomorphism such that f < sup > 2 </ sup > is the identity endomorphism of M.
If we understand the names, we should understand the information they carry, namely the identity of their bearers, and if we grasp their identity, we should understand automatically whether the statement is true or false.
In particular, if S and T ( subgroups now ) intersect only in the identity, then every element of ST has a unique expression as a product st with s in S and t in T. If S and T also permute, then ST is a group, and is called a Zappa-Szep product.
Zahi Hawass, the former chief of Egypt's Supreme Council of Antiquities, asked that the stele be repatriated to Egypt, urging in comments to reporters: " If the British want to be remembered, if they want to restore their reputation, they should volunteer to return the Rosetta Stone because it is the icon of our Egyptian identity ".

If and we
If we let them go, they won't stay away, they'll find men to ride with them and they'll be back.
If we was both armed, you wouldn't talk so tough ''.
If we have to we'll take him apart and see what he's made of ''!!
If we look at recent art we find it preoccupied with form.
If we were creating a wholly new society, we could insist that our social, political, economic and philosophic institutions foster rather than hamper man ; ;
If we want respect from ourselves or others, we will have to earn it.
If we cannot stop warfare in our own economic system, how can we expect to abolish it internationally??
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 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 you had screamed right there in the street where we stood, I could not have felt more fear.
If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.
If we grasp this opportunity to build an age of productive partnership between the less fortunate nations and those that have already achieved a high state of economic advancement, we will make brighter the outlook for a world order based upon security and freedom.
If art is to release us from these postulated things ( things we must think symbolically about ) and bring us back to the ineffable beauty and richness of the aesthetic component of reality in its immediacy, it must sever its connection with these common sense entities ''.
If he's going to the St. Louis convention as a delegate we ought to know it.
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 we break the minister to our bit, we are buying back our own sins.

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