* 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.

Consider the subset sum problem, an example of a problem that is easy to verify, but whose answer may be difficult to compute.

Consider a function with its corresponding graph as a subset of the Cartesian product.

Consider an open subset U of the complex plane C. Let a be an element of U, and f: U

Consider the theory obtained by adding a new constant symbol ε to the language and adjoining to Σ the axiom ε > 0 and the axioms ε < 1 / n for all positive integers n. Clearly, the standard real numbers R are a model for every finite subset of these axioms, because the real numbers satisfy everything in Σ and, by suitable choice of ε, can be made to satisfy any finite subset of the axioms about ε.

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

Consider the translates t + N of this subset.

Consider a subset and a mapping function

Consider on K the metric induced by the uniform distance.

Consider a pseudo random number generator ( PRNG ) function P ( key ) that is uniform on the interval 2 < sup > b </ sup > − 1.

Consider that even the most rare events on Earth can happen multiple times and independent of one another.

Consider the following statement in the circumstance of sorting apples on a moving belt:

For example: Consider first a classical computer that operates on a three-bit register.

Consider the distribution on the figure.

Consider now the acceleration due to the sphere of mass M experienced by a particle in the vicinity of the body of mass m. With R as the distance from the center of M to the center of m, let ∆ r be the ( relatively small ) distance of the particle from the center of the body of mass m. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass M. If the body of mass m is itself a sphere of radius ∆ r, then the new particle considered may be located on its surface, at a distance ( R ± ∆ r ) from the centre of the sphere of mass M, and ∆ r may be taken as positive where the particle's distance from M is greater than R. Leaving aside whatever gravitational acceleration may be experienced by the particle towards m on account of ms own mass, we have the acceleration on the particle due to gravitational force towards M as:

Consider a traveling transverse wave ( which may be a pulse ) on a string ( the medium ).

Consider the following operation on an arbitrary positive integer:

Consider the drug testing example in the article on Bayes ' theorem.

Argument from rarity – Consider this case: a lottery winner is accused of cheating, based on the improbability of winning.

Consider a particle P that moves on the surface of a circular cylinder, it is possible to align the Z axis of the fixed frame F with the axis of the cylinder.

Consider an attack on the ciphertext string " WNAIW " encrypted using a Vigenère cipher with a five letter key.

Consider, for instance, these remarks in the introduction to Hegel's Lectures on the Philosophy of History:

" Mother Maria Marthe ( Lilia Skala, called " Mother Maria "), responds by asking him to read another Bible verse from the Sermon on the Mount: " Consider the lilies of the field, how they grow ; they toil not, neither do they spin.

After a week on the run, he meets the Artful Dodger, who beckons Oliver to join him (" Consider Yourself ").

Consider a capacitor of capacitance C, holding a charge + q on one plate and − q on the other.

Consider a configuration in which the rapidly moving material down the chute impinges on an obstruction wall erected perpendicular at the end of a long and steep channel.

Consider an equilateral triangle with three spins, one on each vertex.