* 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:

* 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.

Consider first-order linear ODEs of the general form:

Consider the unitary form defined above for the DFT of length N, where

Consider the relation involving three roles that people might play, expressed in a statement of the form " X thinks that Y likes Z ".

Consider, for example, a recurrence relation of the form

Consider a system of n linear equations for n unknowns, represented in matrix multiplication form as follows:

Consider the polynomial ring R, and the irreducible polynomial The quotient space is given by the congruence As a result, the elements ( or equivalence classes ) of are of the form where a and b belong to R. To see this, note that since it follows that,,, etc.

Consider the restrictions on x < sub > 1 </ sub >, x < sub > 2 </ sub >, y < sub > 1 </ sub >, y < sub > 2 </ sub > required to make u and v form an orthonormal pair.

Consider a dynamical system of the form x < nowiki >'</ nowiki >

Consider the problem of finding solutions of the form ƒ ( r, θ, φ ) = R ( r ) Y ( θ, φ ).

Pragmaticism was originally enounced in the form of a maxim, as follows: Consider what effects, that might conceivably have practical bearings, you conceive the objects of your conception to have.

Consider solutions in which a fixed wave form ( given by f ( X )) maintains its shape as it travels to the right at phase speed c. Such a solution is given by ( x, t )

The first of these three identities says that the 0 form a representation of the ordinary Lie algebra spanned by E ( Consider the 0 as vectors on which the E act.

They find that orienting strategies should be understood as metatheories: " Consider the very large proportion of sociological theory that is in the form of metatheory.

Consider the illustration, depicting a plane intersecting a cone to form an ellipse ( the interior of the ellipse is colored light blue ).

Consider a quasilinear PDE of the form

Consider now a PDE of the form

Consider now the following form of v ( r-R ),

Consider a linear model of the form

Consider that the nervous system in animals is a form of hybrid computer.

Consider a linear non-homogeneous ordinary differential equation of the form

Consider an ordinary differential equation of the form

Consider first the usual parametric form of a straight line: