Consider a wave packet as a function of position x and time t: α ( x, t ).

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

Consider the logarithm function: For any fixed base b, the logarithm function log < sub > b </ sub > maps from the positive real numbers R < sup >+</ sup > onto the real numbers R ; formally:

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 a function that takes no parameters and returns input from the keyboard.

Consider a wave function that is a sum of many waves, however, we may write this as

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

Consider the recursion equations for the factorial function f:

Consider a function that reads the next line of text from a given file:

Consider the complex Hilbert space L < sup > 2 </ sup >( R ), and the operator which multiplies a given function by x:

Consider a function of jump process.

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 a differentiable function ƒ ( x ) whose derivative is ƒ '( x ).

Consider the vector-valued function F from R < sup > 2 </ sup > to R < sup > 2 </ sup > defined by

Consider an open set on the real line and a function f defined on that set with real values.

Consider, for purposes of illustration, a mountainous landscape M. If f is the function sending each point to its elevation, then the inverse image of a point in ( a level set ) is simply a contour line.

Consider two waveforms f and g. By calculating the convolution, we determine how much a reversed function g must be shifted along the x-axis to become identical to function f. The convolution function essentially reverses and slides function g along the axis, and calculates the integral of their ( f and the reversed and shifted g ) product for each possible amount of sliding.

Consider the complex logarithm function log z.

Consider the function

The Mind in Consider Phlebas is also described as having internal power sources which function as back-up shield generators and space propulsion, and seeing the rational, safety-conscious thinking of Minds, it would be reasonable to assume that all Minds have such features, as well as a complement of drones and other remote sensors as also described.

Geometric arrangement for Fresnel's calculation Consider the case of a point source located at a point P < sub > 0 </ sub >, vibrating at a frequency f. The disturbance may be described by a complex variable U < sub > 0 </ sub > known as the complex amplitude.

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 vectors ( functions ) f and g defined by f ( t ) := e < sup > it </ sup > and g ( t ) := e < sup >− it </ sup >.

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

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 a set of functions f < sub > 1 </ sub >, f < sub > 2 </ sub >,..., f < sub > n </ sub >.

Consider for instance the map f: ( 0, 1 ) → R < sup > 2 </ sup > with f ( t )

Consider the functions f and g from the natural numbers to the natural numbers defined as follows:

Consider the GNS representation π < sub > f </ sub > with cyclic vector ξ.

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 )

Consider also a goods allocation that is vector-valued and size ( which permits number of goods ) and assume it is piecewise continuous with respect to its arguments.

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

Consider for instance the sequence defined by and.

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

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 a language ( such as English ) in which the arithmetical properties of integers are defined.

Example Consider the bilateral shift T on l < sup > 2 </ sup >( Z ) defined by

Consider a simple 1D advection problem defined by the following partial differential equation

Consider an integer N and a non-negative monotone decreasing function f defined on the unbounded interval < nowiki >

Consider a Borel regular measure μ on X, and a functional ψ defined by

Consider a bounded linear transformation T defined everywhere over a general Banach space.

Consider a set of points R ( R is a vector depicting a point in a Bravais lattice ) constituting a Bravais lattice, and a plane wave defined by:

Consider a symmetric game with a smooth payoff function defined over actions of two or more players.

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

Let p be a point of M. Consider the space consisting of smooth maps defined in some neighborhood of p. We define an equivalence relation on as follows.

Consider the function ' of the variable ℝ < sup > n </ sup > defined by

Consider now the ring R defined as the intersection

Consider a real valued function ƒ of a real variable x, defined in a neighborhood of the point x < sub > 0 </ sub > in which ƒ is discontinuous.