Let X be some repeatable process, and i be some point in time after the start of that process.

* Theorem Let X be a normed space.

* Corollary Let X be a reflexive normed space and Y a Banach space.

* Corollary Let X be a reflexive normed space.

Let X and Y be two K-vector spaces.

Let V, W and X be three vector spaces over the same base field F. A bilinear map is a function

* Let X be a simply ordered set endowed with the order topology.

Let X denote a Cauchy distributed random variable.

Let X be a nonempty set, and let.

: Theorem on projections: Let the function f: X → B be such that a ~ b → f ( a )

Let X be a finite set with n elements.

" Let X be the unit Cartesian square ×, and let ~ be the equivalence relation on X defined by ∀ a, b ∈ (( a, 0 ) ~ ( a, 1 ) ∧ ( 0, b ) ~ ( 1, b )).

Let X < sub > i </ sub > be the measured weight of the ith object, for i

Let X be a topological space, and let x < sub > 0 </ sub > be a point of X.

Let be the conditional probability distribution function of Y given X.

Let ƒ be a function whose domain is the set X, and whose range is the set Y.

Let ( X < sub > i </ sub >, f < sub > ij </ sub >) be an inverse system of objects and morphisms in a category C ( same definition as above ).

* Let the index set I of an inverse system ( X < sub > i </ sub >, f < sub > ij </ sub >) have a greatest element m. Then the natural projection π < sub > m </ sub >: X → X < sub > m </ sub > is an isomorphism.

Let there be a finite sequence of positive integers X

Let X be a measurable space, let μ be a measure on X, and let N be a measurable set in X.

Let the quantities u and v be the horizontal and vertical components of the velocity field of a steady incompressible, irrotational flow in two dimensions.

Let u, v be arbitrary vectors in a vector space V over F with an inner product, where F is the field of real or complex numbers.

Let the curve be a unit speed curve and let t = u × T so that T, u, t form an orthonormal basis: the Darboux frame.

Let m < sub > 1 </ sub > and m < sub > 2 </ sub > be the masses, u < sub > 1 </ sub > and u < sub > 2 </ sub > the velocities before collision, and v < sub > 1 </ sub > and v < sub > 2 </ sub > the velocities after collision.

Let Y = u ( X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub >) be a statistic whose pdf is g ( y ; θ ).

Let u = x < sup > 3 </ sup >.

Let y be a function given by the sum of two functions u and v, such that:

Let x: y: z be a variable point in trilinear coordinates, and let u

Let vectors < u > a </ u >, < u > b </ u >, < u > c </ u > and < u > h </ u > determine the position of each of the four orthocentric points and let < u > n </ u > = (< u > a </ u > + < u > b </ u > + < u > c </ u > + < u > h </ u >) / 4 be the position vector of N, the common nine-point center.

Let the input power to a device be a force F < sub > A </ sub > acting on a point that moves with velocity v < sub > A </ sub > and the output power be a force F < sub > B </ sub > acts on a point that moves with velocity v < sub > B </ sub >.

Let the ship moves with velocity v. In the ship reference frame, capturing the 4 hydrogen we losing a momentum:

Let A be an m × n matrix, with column vectors v < sub > 1 </ sub >, v < sub > 2 </ sub >, ..., v < sub > n </ sub >.

Let x = x ( u, v, w ), y = y ( u, v, w ), z = z ( u, v, w ) be defined and smooth in a domain containing, and let these equations define the mapping of into.

Let v be the last vertex before u on this path.

Here is Leibniz's argument: Let u ( x ) and v ( x ) be two differentiable functions of x.

Let f = uv and suppose u and v are positive functions of x.

Let u and v be continuous functions in x, and let dx, du and dv be infinitesimals within the framework of non-standard analysis, specifically the hyperreal numbers.

Let v ∈ T < sub > p </ sub > M be a tangent vector to the manifold at p. Then there is a unique geodesic γ < sub > v </ sub > satisfying γ < sub > v </ sub >( 0 )

Let v be an arbitrary vector in V. There exist unique scalars such that:

Let S be the number of particles in the swarm, each having a position x < sub > i </ sub > ∈ < sup > n </ sup > in the search-space and a velocity v < sub > i </ sub > ∈ < sup > n </ sup >.

Proof: Let ( v, λ ) be an eigenvector-eigenvalue pair for a matrix A.

Let s be the function mapping the sphere to itself, and let v be the tangential vector function to be constructed.