* Consider a set with three elements, A, B, and C. The following operation:

* Consider the set of all functions from the real number line to the closed unit interval, and define a topology on so that a sequence in converges towards if and only if converges towards for all.

* Consider the set K of all functions ƒ: → satisfying the Lipschitz condition | ƒ ( x ) − ƒ ( y )| ≤ | x − y | for all x, y ∈.

* Consider the modulo 2 equivalence relation on the set of integers: if and only if their difference is an even number.

Consider all the functions φ: G → R such that the set

Consider a function from a metric space M to a topological space V, and a point c of M. We direct the set M

Consider some set P and a binary relation ≤ on P. Then ≤ is a preorder, or quasiorder, if it is reflexive and transitive, i. e., for all a, b and c in P, we have that:

Consider the set of pulleys that form the moving block and the parts of the rope that support this block.

* Chapter 7 divides humility into twelve degrees, or steps in the ladder that leads to heaven :( 1 ) Fear God ; ( 2 ) Substitute one's will to the will of God ; ( 3 ) Be obedient to one's superior ; ( 4 ) Be patient amid hardships ; ( 5 ) Confess one's sins ; ( 6 ) Accept oneself as a " worthless workman "; ( 7 ) Consider oneself " inferior to all "; ( 8 ) Follow examples set by superiors ; ( 9 ) Do not speak until spoken to ; ( 10 ) Do not laugh ; ( 11 ) Speak simply and modestly ; and ( 12 ) Be humble in bodily posture.

That means that some member of P ( S ), i. e., some subset of S, is not in the image of f. Consider the set:

Consider the ( possibly proper ) class B defined such for every set y, y is in B if and only if there is an x in A with F < sub > P </ sub >( x ) = y.

Consider the approach we would take classically-we pick one block at random, and then perform a normal search through the rest of the blocks ( in set theory language, the compliment ).

Consider Phlebas is Banks's first published science fiction novel set in the Culture, and takes its title from a line in T. S. Eliot's poem The Waste Land.

The Idiran-Culture War is a major fictional conflict between the Idiran Empire and the Culture in the midst of which Iain M. Banks ' science fiction novel Consider Phlebas is set.

Consider the set of unlabelled binary trees.

Consider a set of functions f < sub > 1 </ sub >, f < sub > 2 </ sub >,..., f < sub > n </ sub >.

Consider the set W of all deductively closed sets of formulas, ordered by inclusion.

Consider the set of all trial probability distributions that encode the prior data.

Consider a graph G with vertices V, each numbered 1 through N. Further consider a function shortestPath ( i, j, k ) that returns the shortest possible path from i to j using vertices only from the set

Consider, for example, the generalized hypergraph whose vertex set is and whose edges are and.

Consider a set of square-integrable functions with values in,

Consider the language of set theory with extra constant symbols c < sub > 1 </ sub >, c < sub > 2 </ sub >, ... for each positive integer.

Consider the set of all nilpotent elements of R, which will be called the nilradical of R ( and will be denoted by N ( R )).

Consider a gas in a box of set volume.

Consider the process illustrated in Fig. 2.1, consisting of R distinct stages.

Consider a test apparatus consisting of a closed and well insulated cylinder equipped with a piston.

Consider a population consisting of the following eight values:

Again we start with a C < sup >∞</ sup > manifold, M, and a point, x, in M. Consider the ideal, I, in C < sup >∞</ sup >( M ) consisting of all functions, ƒ, such that ƒ ( x ) = 0.

Consider a sequence consisting of real numbers.

If S is compact but not closed, then it has an accumulation point a not in S. Consider a collection consisting of an open neighborhood N ( x ) for each x ∈ S, chosen small enough to not intersect some neighborhood V < sub > x </ sub > of a.

Consider a mechanical system consisting of two partial systems A and B which interact with each other only during a limited time.

Consider for example the same task as above but with an array consisting of 1000 numbers instead of 100, and where all numbers have the value 1.

Consider a simple clock consisting of two mirrors A and B, between which a light pulse is bouncing.

Consider the subset C of B, consisting of those B elements, which satisfy monic polynomial equations over A:

Consider an-dimensional space, foliated as a product by subspaces consisting of points whose first co-ordinates are constant.

Consider a divider consisting of a resistor and capacitor as shown in Figure 3.

Consider a test consisting of items,.

Consider a portfolio P consisting of C < sub > i </ sub > amount of each Arrow security A < sub > i </ sub >.

Consider the unit circle S, and the action on S by a group G consisting of all rational rotations.

Consider a neutral plasma, consisting of a gas of positively charged ions and negatively charged electrons.

Consider a two-body system consisting of a central body of mass M and a much smaller, orbiting body of mass m, and suppose the two bodies interact via a central, inverse-square law force ( such as gravitation ).

Consider an election consisting of five voters and three alternatives, in which three voters prefer A to B and B to C, while two of the voters prefer B to C and C to A.

Consider a simple non-hierarchical Bayesian model consisting of a set of i. i. d.

Consider a discrete charge distribution consisting of N point charges q < sub > i </ sub > with position vectors r < sub > i </ sub >.

Let p be a point of M. Consider the space consisting of smooth maps defined in some neighborhood of p. We define an equivalence relation on as follows.

Consider a trader who has bought a unit portfolio consisting of one contract each for the Red Party, the Blue Party, and the Green Party, at a cost of $ 1.

Consider a game consisting of an employer considering whether to hire a job applicant.

Consider a positive multiplier consisting of a block of 1s surrounded by 0s.