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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, 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 numbers
If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.
If he can't play with Mommy's magazines, he should have some old numbers of his own.
If we are discussing differentiable complex-valued functions, then Af and V are complex vector spaces, and Af may be any complex numbers.
If he does, it's still better than an even chance he won't notice the transposition of the numbers, and if he should notice it, the thing can be passed off as an honest mistake.
* If numbers have mean X, then.
* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.
** If the set A is infinite, then there exists an injection from the natural numbers N to A ( see Dedekind infinite ).
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.
Let ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.
If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.
If the exponent r is even, then the inequality is valid for all real numbers x.
If the convention B < sub > 1 </ sub >=− is used, this sequence is also known as the first Bernoulli numbers ( / in OEIS ); with the convention B < sub > 1 </ sub >=+ is known as the second Bernoulli numbers ( / in OEIS ).
If the shooter rolls one of these numbers on the come-out roll, this establishes the " point "-to " pass " or " win ", the point number must be rolled again before a seven.
If is a convex set, for any in, and any nonnegative numbers such that, then the vector
If n ≥ 1 and is an integer, the numbers coprime to n, taken modulo n, form a group with multiplication as operation ; it is written as ( Z / nZ )< sup >×</ sup > or Z < sub > n </ sub >< sup >*</ sup >.
If the numbers describing the position of the pyramid were changed and this process repeated, the pyramid would appear to move.
From the criterion it also follows that Carmichael numbers are cyclic .< ref > Proof sketch: If is square-free but not cyclic, for two prime factors and of.
This is a Cauchy sequence of rational numbers, but it does not converge towards any rational limit: If the sequence did have a limit x, then necessarily x < sup > 2 </ sup > = 2, yet no rational number has this property.
If x and y are real numbers, and if the graph of y is plotted against x, the derivative measures the slope of this graph at each point.
If we look for solutions that have the form, where C is a constant, we discover the relationship, and thus must be one of the complex numbers or.
If the matrix entries are real numbers, the matrix can be used to represent two linear mappings: one that maps the standard basis vectors to the rows of, and one that maps them to the columns of.
* If we think of as the set of real numbers, then the direct product is precisely just the cartesian product,.
* If we think of as the group of real numbers under addition, then the direct product still consists of.

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