* 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.

Consider the set consisting of

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.

Fundamental group: Consider the category of pointed topological spaces, i. e. topological spaces with distinguished points.

Consider the following examples, created using animated GIFs, wherein a key frame defines the starting and ending points of any smooth transition:

Consider the following example: A game is being played to 9 points.

We say that the number x is a periodic point of period m if f < sup > m </ sup >( x ) = x ( where f < sup > m </ sup > denotes the composition of m copies of f ) and having least period m if furthermore f < sup > k </ sup >( x ) ≠ x for all 0 < k < m. We are interested in the possible periods of periodic points of f. Consider the following ordering of the positive integers:

Consider the solid ball in R < sup > 3 </ sup > of radius π ( that is, all points of R < sup > 3 </ sup > of distance π or less from the origin ).

Consider two points A and B in two dimensional plane flow.

Consider a set of n points in a compact area with approximate diameter d and area approximately d².

Consider all the unordered sets of k points from the n points, of which there are:

Consider a polygon P and a triangle T, with one edge in common with P. Assume Pick's theorem is true for both P and T separately ; we want to show that it is also true to the polygon PT obtained by adding T to P. Since P and T share an edge, all the boundary points along the edge in common are merged to interior points, except for the two endpoints of the edge, which are merged to boundary points.

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

* Consider a Bézier curve with control points.

Consider a topological space, that is, a space with some notion of closeness between points in the space.

Consider the problem of estimating the probability that a test point in N-dimensional Euclidean space belongs to a set, where we are given sample points that definitely belong to that set.

Consider a finite group permuting those indeterminates over K. By standard Galois theory, the set of fixed points of this group action is a subfield of, typically denoted.

Consider the set of all points to be one large partition.

Consider an edge e between two input points p and q which is not an edge of a Delaunay triangulation.

Consider a once-punctured elliptic curve, given as the locus D of complex points satisfying, where and is a complex number.

Consider the first case, with points x = ( x < sub > 1 </ sub >, x < sub > 2 </ sub >, x < sub > 3 </ sub >) and y = ( y < sub > 1 </ sub >, y < sub > 2 </ sub >, y < sub > 3 </ sub >).

Consider the line in the body defined by the two points p and q, which has the Plücker coordinates,

Consider any set of d + 2 points in d-dimensional space.

Consider a set P of n points in the plane.