Judge Birch, a jurist, declared that :< p > If the Act only provided for jurisdiction consistent with Article III, the Act would not be in violation of the principles of separation of powers.

If the conjecture were true, it would be a generalization of Fermat's last theorem, which could be seen as the special case n = 2: if, then.

If the four-color conjecture were false, there would be at least one map with the smallest possible number of regions that requires five colors.

If a definite statement is believed plausible by some mathematicians but has been neither proved nor disproved, it is called a conjecture, as opposed to an ultimate goal: a theorem that has been proved.

If, for some n, such an i doesn't exist, we say that n has infinite total stopping time and the conjecture is false.

If the conjecture is false, it can only be because there is some starting number which gives rise to a sequence which does not contain 1.

If the strong Goldbach conjecture is true, the weak Goldbach conjecture will be true by implication.

This precept, from one of Bacchylides ' extant fragments, was considered by his modern editor, Richard Claverhouse Jebb, to be typical of the poet's temperament: " If the utterances scattered throughout the poems warrant a conjecture, Bacchylides was of placid temper ; amiably tolerant ; satisfied with a modest lot ; not free from some tinge of that pensive melancholy which was peculiarly Ionian ; but with good sense ..."

If Rivers ever did come to access the veiled memory then he does not appear to make a note of it so the nature of the experience is open to conjecture.

The conjecture is stated in terms of three positive integers, a, b and c ( whence comes the name ), which have no common factor and satisfy a + b = c. If d denotes the product of the distinct prime factors of abc, the conjecture essentially states that d cannot be much smaller than c.

If G, H are graphs, we define a map φ: E ( G ) —> E ( H ) to be cycle-continuous if the pre-image of every cycle of H is a cycle of G. A fascinating conjecture of Jaeger asserts that every bridgeless graph has a cycle-continuous mapping to the Petersen graph.

Haupt's critical work is distinguished by a combination of the most painstaking investigation with bold conjecture ; his oft-cited dictum that " If the sense requires it, I am prepared to write Constantinopolitanus where the MSS have the monosyllabic interjection o " well expresses this boldness.

If the Hodge conjecture holds for Hodge classes of degree p, p < n, then the Hodge conjecture holds for Hodge classes of degree 2n − p.

If this conjecture is correct, quipus are the only known example of a complex language recorded in a 3-D system.

If the conjecture is false, a counterexample would take the form of a graph with minimum degree three having no power-of-two cycles.

If π ( x ) is the number of primes up to and including x then the conjecture states that

If the first Hardy – Littlewood conjecture holds, then the first such k-tuple is expected for x greater than 1. 5 × 10 < sup > 174 </ sup > but less than 2. 2 × 10 < sup > 1198 </ sup >.

" Despite its simplicity, it suggests a deeper conjecture: " If is an algebraic extension and if every nonconstant polynomial with coefficients in F has a root in E, is E algebraically closed?

If a lower bound ( for the function value ) could be found for every one of these configurations that was greater than the value of the function for the cubic close packing arrangement, then the Kepler conjecture would be proved.

If the conjecture is true, this would imply the nonexistence of odd perfect numbers.

If the unique games conjecture is true, then it is impossible to approximate MAX 2-SAT, balanced or not, with an approximation constant better than 0. 943 ... in polynomial time.

In mathematics, the Sato – Tate conjecture is a statistical statement about the family of elliptic curves E < sub > p </ sub > over the finite field with p elements, with p a prime number, obtained from an elliptic curve E over the rational number field, by the process of reduction modulo a prime for almost all p. If N < sub > p </ sub > denotes the number of points on E < sub > p </ sub > and defined over the field with p elements, the conjecture gives an answer to the distribution of the second-order term for N < sub > p </ sub >.

If, when this was all over, she found the words to tell him about it, she wondered if he would ever understand.

If you don't leave this country within 3 days, your life will be taken the same as Powell's was.

If we was both armed, you wouldn't talk so tough ''.

If it were the enemy, tactically his position was correct.

If the turn was too tight, a barrel roll would bring them out.

If it were not that I knew who it was I could have mistaken it for my Aunt so well did her clothes fit him.

If Franklin was an authentic genius, then Alexander Hamilton, with his exceptional precocity, consuming energy, and high ambition, was a political prodigy.

`` If you can conveniently let me have twenty dollars '', he wrote one friend in 1791 when he was Secretary of the Treasury.

If an automobile were approaching him, he would know what was required of him, even though he might not be able to act quickly enough.

If living Jews were unavailable for study, the Bible was at hand.

If there was ever a thought in her mind she might devote her life to religion, it was now dispelled.

If his scholarship and formal musicianship were not all they might have been, Mercer demonstrated at an early age that he was gifted with a remarkable ear for rhythm and dialect.

If she were not at home, Mama would see to it that a fresh white rose was there.

If, as Reid says, `` nearly all his poetry was produced when he was not taking opium '', there may be some reason to doubt that he was under its influence in the period from 1896 to 1900 when he was writing the poems to Katie King and making plans for another book of verse.

If Robinson was a liar and a slanderer, he was also a very canny gentleman, for nothing that Pike could do would pry so much as a single word out of him.

If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.

If the historian was convinced of his own correctness, then he should not allow his vision to become fogged by disturbing facts.

If their schedules were to synchronize, there was no point in wasting time.

If he had any worries, it was only the small ones, about Mother in New York, and his daughter Edwina and what she might be doing at this hour, with her Aunt Asia, in Philadelphia.