* 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.

Consider adopting a system of holidays in which time off is granted with an eye to minimum inconvenience to the operation of the plant.

Consider a shear field with a height of H and a cross-sectional area of A opposed by a manometer with a height of H ( referred to the same base as H ) and a cross-sectional area of A.

Consider the assembly of a car: assume that certain steps in the assembly line are to install the engine, install the hood, and install the wheels ( in that order, with arbitrary interstitial steps ); only one of these steps can be done at a time.

Consider a speech signal reduced to packets, and forced to share a link with bursty data traffic ( traffic with some large data packets ).

Consider a complete orthonormal system ( basis ),, for a Hilbert space H, with respect to the norm from an inner product.

Consider the real line with its ordinary topology.

( Consider 1 / 0, which is defined with the value of infinity, vs. 0 / 0, which is undefined.

Consider a physical system that acts as a linear filter, such as a system of springs and masses, or an analog electronic circuit that includes capacitors and / or inductors ( along with other linear components such as resistors and amplifiers ).

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

Consider a collection of particles performing a random walk in one dimension with length scale and time scale.

< li > Consider the group ( Z < sub > 6 </ sub >, +), the integers from 0 to 5 with addition modulo 6.

* The Infinite Moment ( 1961 ) ( US edition of Consider Her Ways, with two stories dropped, two others added )

Consider the following example ( in Kwakw ' ala, sentences begin with what corresponds to an English verb ):

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

Consider two noninteracting systems and, with respective Hilbert spaces and.

Consider as above systems and each with a Hilbert space,.

Consider two ISPs, A and B, which each have a presence in New York, connected by a fast link with latency 5 ms ; and which each have a presence in London connected by a 5 ms link.

Consider the following: if the typical user is searching with term " A ", would they also want resources tagged with term " B "?

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 linear differential equation with constant coefficients

Consider the time series of an independent variable and a dependent variable, with observations sampled at discrete times.