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Page "Polynomial" ¶ 35
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If and however
If, however, the child is weak, overweight, or afraid, more help will be needed.
If, however, it would help to intensify your anguish, I can delimit the powers of a few of the divinities you've affronted and describe the punishment they meted out in one analogous instance.
If, however, the figure to be discerned were complicated, composed of several interlocking subfigures, and so on, even the tracing process failed him, and he could not focus even relatively simple shapes among its parts.
If the retailer and hotelman's downtown unit sales have been decreasing, however, his dollar volume continues to rise, and it is dollars which you put in the bank.
If the distant patron of the suburban branch has been frightened away from downtown by traffic problems, however, the city store can only pressure the politicians to do something about the highways or await the completion of the federal highway program.
If, however, we are seeking the optimal R-stage policy for a given feed state, only one search for a maximum is required at the final step.
If the photographically realistic continuity of dreams, however bizarre their combinations, denies that it is purely a composition of the brain, it must be compounded from views of diverse realities, although some of them may never be encountered in what we are pleased to call the real life.
If, however, the numbers are referring to allies it could possibly include forces from Tyre, Judah, Edom, and Moab.
If, however, there are no shares left when the chain is founded, then the founding player does not receive the free share.
If, however, one picks non-optimally, after improving a sub-optimal component and moving on to improve a more optimal component, one can see an increase in return.
If, however, a layer of paper remains stuck to the surface, the adhesive has not failed.
If, however, the court finds that the current dispute is fundamentally distinct from all previous cases ( called a " matter of first impression "), judges have the authority and duty to make law by creating precedent.
If however it was possible to have two of any one kind of fruit there would be 3 more combinations: one with two apples, one with two oranges, and one with two pears.
If a cabal can be implicated in a sequence of events, there is always the hope, however tenuous, of being able to break the cabal's power – or joining it and exercising some of that power oneself.
If however it has already saved its life by self-castration and is again pursued, then it stands up and reveals that it offers no ground for their eager pursuit, and releases the hunters from all further exertions, for they esteem its flesh less.
If people with cholera are treated quickly and properly, the mortality rate is less than 1 %; however, with untreated cholera, the mortality rate rises to 50 – 60 %.
If the function f is not linear ( i. e. its graph is not a straight line ), however, then the change in y divided by the change in x varies: differentiation is a method to find an exact value for this rate of change at any given value of x.
If in the above example Mary had overpaid, paying £ 750 for the watch, her damages in contract would still be £ 450 ( giving him the item he contracted to buy ), however in tort damages are £ 700.
If this happens to all industries however, everyone would be worse off than if they had been subject to the rigours of market competition.
His government has also been condemned for allegedly arming and financing the insurgency in Somalia ; the United States is considering labeling Eritrea a " State Sponsor of Terrorism ," however, many experts on the topic have shied from this assertion, stating that " If there is one country where the fighting of extremists and terrorists was a priority when it mattered, it was Eritrea.
Frege, however, did not conceive of objects as forming parts of senses: If a proper name denotes a non-existent object, it does not have a reference, hence concepts with no objects have no truth value in arguments.
If the occulting object has an atmosphere, however, some of the luminosity of the star can be refracted into the volume of the umbra.
If they had gone it alone, the IRB and the Volunteers would possibly have come to their aid ; however, the IRB leaders met with Connolly in January 1916 and convinced him to join forces with them.
If, however, the firm is not a perfect competitor in the input markets, then the above conclusions are modified.
If this is done on fractals, however, no new detail appears ; nothing changes and the same pattern repeats over and over, or for some fractals, nearly the same pattern reappears over and over.

If and set
If Mahzeer was planning to set up the prime minister for Muller he would have to do it in the next few minutes.
If the defendant pleads not guilty, a date is set for a preliminary hearing or a trial.
If they don't then for the algorithm to be effective it must provide a set of rules for extracting a square root.
If we cannot make explicit choices, how do we know that our set exists?
If we try to choose an element from each set, then, because X is infinite, our choice procedure will never come to an end, and consequently, we will never be able to produce a choice function for all of X.
** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.
** If the set A is infinite, then there exists an injection from the natural numbers N to A ( see Dedekind infinite ).
If the automorphisms of an object X form a set ( instead of a proper class ), then they form a group under composition of morphisms.
* If a set S is in M and S is congruent to T then T is also in M and a ( S )
* 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 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:
* If you want to be happy, set a goal that commands your thoughts, liberates your energy, and inspires your hopes.
If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.
If X and Y are Banach spaces over the same ground field K, the set of all continuous K-linear maps T: X → Y is denoted by B ( X, Y ).
If the score is tied the set is halved.
If each player wins a set, or both sets end tied, there is a 3-end tiebreaker to determine a winner.
If a node has fewer than two children, some of the child pointers may be set to a special null value, or to a special sentinel node.
Some authors require in addition that μ ( C ) < ∞ for every compact set C. If a Borel measure μ is both inner regular and outer regular, it is called a regular Borel measure.
In the words of Geoffrey Crowther, then editor of The Economist, " If the economic relationships between nations are not, by one means or another, brought fairly close to balance, then there is no set of financial arrangements that can rescue the world from the impoverishing results of chaos.
If, for instance, an addition operation was requested, the arithmetic logic unit ( ALU ) will be connected to a set of inputs and a set of outputs.
If the addition operation produces a result too large for the CPU to handle, an arithmetic overflow flag in a flags register may also be set.

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