Formally, let S and T be finite sets and let F =

If R is a ring, let R denote the ring of polynomials in the indeterminate X over R. Hilbert proved that if R is " not too large ", in the sense that if R is Noetherian, the same must be true for R. Formally,

Formally, let P be an expression in which the variable x is free.

Formally, let be a surjective homomorphism.

Formally, let be a stochastic process and let represent the cumulative distribution function of the joint distribution of at times.

Formally, let f: < sup > n </ sup > → be the cost function which must be minimized.

Formally, let P and Q be abelian categories, and let

Formally, let A be a real matrix of which we want to compute the eigenvalues, and let A < sub > 0 </ sub >:= A.

Formally, let G be a Coxeter group with reduced root system R and k < sub > v </ sub > a multiplicity function on R ( so k < sub > u </ sub > = k < sub > v </ sub > whenever the reflections σ < sub > u </ sub > and σ < sub > v </ sub > corresponding to the roots u and v are conjugate in G ).

Formally, let p ( x, y ) be a complex polynomial in the complex variables x and y.

Formally, for received words, let denote the Hamming distance between and, that is, the number of positions in which and differ.

Formally, let p and q be two nonzero polynomials, respectively of degree m and n. Thus:

Formally, let P be a poset ( partially ordered set ), and let F be a filter on P ; that is, F is a subset of P such that:

Formally, let denote the pairwise score for against.

Formally, let X be any scheme and S be a sheaf of graded-algebras ( the definition of which is similar to the definition of-modules on a locally ringed space ): that is, a sheaf with a direct sum decomposition