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.

If these ratios are averaged using an arithmetic mean ( a common error ), high data points are given greater weights than low data points.

If all weights () are

( If the graph has no weights, 1 indicates an edge, 0 indicates no edge.

If all the weights are equal, then the weighted mean is the same as the arithmetic mean.

If all of the are drawn from the same distribution and the integer weights indicate frequency of occurrence in the sample, then the unbiased estimator of the weighted population variance is given by

If they are unsuccessful at that weight, they have the option of reattempting at that weight or trying a heavier weight after any other competitors have made attempts at the previous weight or any other intermediate weights.

If the array of weights consists of N weights spaced evenly over the length L

If the edge weights are not unique, only the ( multi -) set of weights in minimum spanning trees is unique, that is the same for all minimum spanning trees.

If a tri-drive prime mover is utilised, along with tri-axle dollys, weights can reach nearly.

If the person in the chair pulls the weights towards them, they are doing work and their rotational kinetic energy increases.

If the commodity is quantified in weights according to the usage of its traders, its weight must be determined, and if it is quantified through measures, its exact measure should be known.

If daily weights cannot be obtained, diuretics can also be guided by the urinary sodium concentration.

If the weight of a cycle-cover is defined to be the product of the weights of the arcs in each cycle, then

If the weight of a perfect matching that matches to is defined to be the product of the weights of the edges in the matching, then

If the classifier is linear, then the training model is a set of weights used to scale the value in each voxel before summing them to generate a single number that tells us the condition associated with the data set.

Let g be a Lie algebra, h a maximal commutative Lie subalgebra consisting of semi-simple elements ( sometimes called Cartan subalgebra ) and let V be a finite dimensional representation of g. If g is semisimple, then g = g and so all weights on g are trivial.

If V is the adjoint representation of g, its weights are called roots, the weight spaces are called root spaces, and weight vectors are sometimes called root vectors.

where RSS < sub > i </ sub > is the residual sum of squares of model i. If your regression model has been calculated with weights, then replace RSS < sub > i </ sub > with χ < sup > 2 </ sup >, the weighted sum of squared residuals.

If G is a Kac-Moody algebra, then in any irreducible highest weight representation of U < sub > q </ sub >( G ), with highest weight, the multiplicities of the weights are equal to their multiplicities in an irreducible representation of U ( G ) with equal highest weight.

All columns have a range of molecular weights that can be separated. Range of molecular weights that can be separated for each packing material If an analyte is either too large or too small it will be either not retained or completely retained respectively.

If comparable standards are used, this relative data can be used to determine molecular weights within ± 5 % accuracy.