* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )

If the domain of F is a disjoint union of two or more intervals, then a different constant of integration may be chosen for each of the intervals.

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 such an employees association is competing against another union, its leverage may be questioned by unions and then evaluated in a court trial.

If heaven is a state of supernatural happiness and union with God, and hell is understood as a state of torture and separation from God then, in this view, the Limbo of Infants, although technically part of hell ( the outermost part, " limbo " meaning " outer edge " or " hem ") is seen as a sort of intermediate state.

# If A is a disjoint union of countably many disjoint Lebesgue measurable sets, then A is itself Lebesgue measurable and λ ( A ) is equal to the sum ( or infinite series ) of the measures of the involved measurable sets.

A measure μ is continuous from below: If E < sub > 1 </ sub >, E < sub > 2 </ sub >, E < sub > 3 </ sub >, … are measurable sets and E < sub > n </ sub > is a subset of E < sub > n + 1 </ sub > for all n, then the union of the sets E < sub > n </ sub > is measurable, and

If in addition, the subset F is the union of P and − P, we call P a positive cone of F. The nonzero elements of P are called the positive elements of F.

If the negated query can be refuted, i. e., an instantiation for all free variables is found that makes the union of clauses and the singleton set consisting of the negated query false, it follows that the original query, with the found instantiation applied, is a logical consequence of the program.

If the branch grew, it was a good omen for the union and family.

If the subsets of X in Σ correspond to numbers in elementary algebra, then the two set operations union ( symbol ∪) and intersection (∩) correspond to addition and multiplication.

That means, define E ≤ F if E is an initial segment of F and the ordering of the members in E is the same as their ordering in F. If E is a chain in A, then the union of the sets in E can be ordered in a way that makes it a continuation of any set in E ; this ordering is a well ordering, and therefore, an upper bound of E in A.

If such a union of human and divine occurred, Nestorius believed that Christ could not truly be con-substantial with God and con-substantial with us because he would grow, mature, suffer and die ( which Nestorius argued God cannot do ) and also would possess the power of God that would separate him from being equal to humans.

If the union rate is $ 60 per page and 20 measures were orchestrated then the orchestrator's bill would be $ 300 plus 10 % for health and pension.

If the employees are unrepresented and the employer agrees, the NMB may certify the union based on the authorization cards alone.

If the employer refuses to recognize the union, the union can be certified through a secret-ballot election conducted by the NLRB.

If such a union of human and divine occurred, Nestorius believed that Christ could not truly be con-substantial with God and con-substantial with us because he would grow, mature, suffer and die ( which he said God cannot do ) and also would possess the power of God that would separate him from being equal to humans.

If any State in the Union will declare that it prefers separation with the first alternative, to a continuance in union without it, I have no hesitation in saying, ' let us separate '.

If there were not, then the entire graph would be the union of finitely many finite sets, and thus finite, contradicting the assumption that the graph is infinite.

If a collective bargaining agreement is in effect, and it contains a " no-strike clause ", a strike during the life of the contract could result in the firing of all striking employees which could result in dissolution of that union.

If a collective bargaining agreement is in effect, and it contains a " no-strike clause ", a strike during the life of the contract could result in the firing of all striking employees which could result in dissolution of that union.

If the intervals in the above definition of the step function are disjoint and their union is the real line, then for all

If we cannot stop warfare in our own economic system, how can we expect to abolish it internationally??

If the points aren't thrown all the way, the Turnout cannot be locked, and in turn, the signal cannot be cleared.

`` If we cannot tell evil, horror, and insanity from nonsense, what is the future of humor and comedy ''??

If a litigant chooses to enforce a Federal right in a State court, he cannot be heard to object if he is treated exactly as are plaintiffs who press like claims arising under State law with regard to the form in which the claim must be stated -- the particularity, for instance, with which a cause of action must be described.

If the patient can perceive figure kinesthetically when he cannot perceive it visually, then, it would seem, the sense of touch has immediate contact with the spatial aspects of things in independence of visual representations, at least in regard to two dimensions, and, as we shall see, even this much spatial awareness on the part of unaided touch is denied by the authors.

If the latter knows nothing about the absent sitter except his name ( given by the experimenter ), he cannot possibly give any clues, conscious or unconscious, far less ask leading questions.

If we cannot make explicit choices, how do we know that our set exists?

If there is an overabundance of food hunted, the arctic fox will bury what the family cannot eat.

If the daughter is an only child or her sisters are deceased and have no living issue, she ( or her heir ) is vested with the title ; otherwise, since a peerage cannot be shared nor divided, the dignity goes into abeyance between the sisters or their heirs, and is held by no one.

If the assets used are not identical ( so a price divergence makes the trade temporarily lose money ), or the margin treatment is not identical, and the trader is accordingly required to post margin ( faces a margin call ), the trader may run out of capital ( if they run out of cash and cannot borrow more ) and go bankrupt even though the trades may be expected to ultimately make money.

If nature cannot err, then there are no paradoxes in it ; to Hobbes, the paradox is a form of the absurd, which is inconsistency: " Natural sense and imagination, are not subject to absurdity " and " For error is but a deception ...

If we cannot stay here alive, then we will stay here dead.

If a pair cannot hit downwards, they will use flat strokes in an attempt to gain the attack.

But this destruction, coupled with a protracted siege of Rain ( 9 – 16 July ), caused Prince Eugene to lament "... since the Donauwörth action I cannot admire their performances ", and later to conclude " If he has to go home without having achieved his objective, he will certainly be ruined.

* Indivisibility of certain goods: If a person wants to buy a certain amount of another's goods, but only has for payment one indivisible unit of another good which is worth more than what the person wants to obtain, a barter transaction cannot occur.

If the remaining array to be searched is reduced to zero, then the key cannot be found in the array and a special " Not found " indication is returned.

If players cannot move either die in a roll, given the position of their checkers then that turn is over and the turn passes to the opponent.

If the Crawford rule is in effect, then another option is the Holland rule, which stipulates that after the Crawford game, a player cannot double until after at least two rolls have been played by each side.

If we look at this situation from far above, so that we cannot see the supporters, we see the large balloon as a small object animated by erratic movement.

If a newer software version cannot save files that can be read by the older version, it is not backward compatible with the older version, although it may provide an irreversible upgrade capability for the old files.

If a Banach algebra has unit 1, then 1 cannot be a commutator ; i. e., for any x, y ∈ A.

If a bookmaker follows the rules of the Bayesian calculus in the construction of his odds, a Dutch book cannot be made.

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