Consider an unsorted database with N entries.

Consider the problem of determining the index of the database entry which satisfies some search criterion.

Consider a dataset represented as a matrix ( or a database table ), such that each row represents a set of attributes ( or features or dimensions ) that describe a particular instance of something.

Consider a database of sales, perhaps from a store chain, classified by date, store and product.

Consider a customer purchasing an item which costs five pence, who possesses several silver sixpence coins.

Consider, for example, a customer service department — where imaging, document management, and workflow could be combined to allow agents to better resolve customer inquiries.

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

* Consider now L = Q ( ³ √ 2, ω ), where ω is a primitive third root of unity.

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 Peter Unger's example of a cloud ( from his famous 1980 paper, " The Problem of the Many "): it's not clear where the boundary of a cloud lies ; for any given bit of water vapor, one can ask whether it's part of the cloud or not, and for many such bits, one won't know how to answer.

Consider, also, that all English speakers often pronounce ' Z ' where ' S ' is spelled, almost always when a noun ending in a voiced consonant or a liquid is pluralized, for example " seasons ", " beams ", " examples ", etc.

Consider the case where the far end of the cable is shorted ( that is, it is terminated into zero ohms impedance ).

Consider the plane spanned by and, where is a ket in the subspace perpendicular to.

Consider a quantum ensemble of size N with occupancy numbers n < sub > 1 </ sub >, n < sub > 2 </ sub >,..., n < sub > k </ sub > corresponding to the orthonormal states, respectively, where n < sub > 1 </ sub >+...+ n < sub > k </ sub >

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 simple experiment where a fair coin is tossed four times.

Consider a number n > 0 in base b ≥ 2, where it is written in standard notation with k + 1 digits a < sub > i </ sub > as:

: Example: Consider a scenario where a legitimate party called Alice encrypts messages using the cipher-block chaining mode.

Consider for example, the sharing of food in some hunter-gatherer societies, where food-sharing is a safeguard against the failure of any individual's daily foraging.

Consider the simple case of two-body system, where object A is moving towards another object B which is initially at rest ( in any particular frame of reference ).

Consider a 10 year mortgage where the principal amount P is $ 200, 000 and the annual interest rate is 6 %.

Consider a simple banking application where two users have access to the funds in a particular account.

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 a random walk on the number line where, at each step, the position ( call it x ) may change by + 1 ( to the right ) or-1 ( to the left ) with probabilities:

Consider a system where the gun and shooter have a combined mass M and the bullet has a mass m. When the gun is fired, the two systems move away from one another with new velocities V and v respectively.

Consider a circuit where R, L and C are all in parallel.

Consider an MDCT with 2N inputs and N outputs, where we divide the inputs into four blocks ( a, b, c, d ) each of size N / 2.

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 the physical model of the citizenship of human beings in the early 21st century, where about 30 % are Indian and Chinese citizens, about 5 % are American citizens, about 1 % are French citizens, and so on.

Consider a social network, where the graph ’ s vertices represent people, and the graph ’ s edges represent mutual acquaintance.

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 three colored blocks ( red, green, and blue ), initially placed in the order RGB.

Consider the direct system composed of the groups Z / p < sup > n </ sup > Z and the homomorphisms Z / p < sup > n </ sup > Z → Z / p < sup > n + 1 </ sup > Z which are induced by multiplication by p. The direct limit of this system consists of all the roots of unity of order some power of p, and is called the Prüfer group Z ( p < sup >∞</ sup >).

Consider two instructions < tt > i1 </ tt > and < tt > i2 </ tt >, with < tt > i1 </ tt > occurring before < tt > i2 </ tt > in program order.

Consider this second order ODE:

A partition of a set S is a pairwise disjoint set of non-empty subsets, called " parts " or " blocks ", whose union is all of S. Consider a finite set that is linearly ordered, or ( equivalently, for purposes of this definition ) arranged in a cyclic order like the vertices of a regular n-gon.

Consider that, if an external attacker did not know the port knock sequence, even the simplest of sequences would require a massive brute force effort in order to be discovered.

Consider a ( multiplicative ) cyclic group of order, and with generator.

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 ).

Consider the following system of first order partial differential equations for unknown functions,, where

Consider, for example, the group generated by 2 modulo ( the order of the group is, 2

Consider a cyclic group G of order q.

Consider the following expressions from first order logic over a signature containing a constant symbol 0 for the number 0, a unary function symbol s for the successor function and a binary function symbol + for addition.

Consider three colored blocks ( red, green, and blue ), initially placed in the order RGB.

Consider a second order partial differential equation in three variables, such as the two-dimensional wave equation

Consider the timelike congruence generated by some timelike unit vector field X, which we should think of as a first order linear partial differential operator.