Sentence examples for finite sequence of elements from inspiring English sources

If (x 0), … x(m − 1)) is a finite sequence of elements of a BA A, then every element of the subalgebra of A generated by {x 0), … , x(m − 1)} can be written as a sum of monomials e(0)x(0) · … · e(m − 1)x(m − 1) for e in some set of functions mapping m = {0, … , m − 1} into 2 = {0, 1}.

Putnam specifies a finite sequence of elements (a vector) for the description of the meaning of every term in the language.

A sequence type is the type of finite sequences of elements of a type which may include an empty sequence.

For any set S we denote by S* the set of all finite sequences of elements of S, including the empty sequence.

Finite sequences of elements of Ω are called positions; they record where a play might have got to by a certain time.

A string on an alphabet Σ is a finite, possibly empty, sequence of elements of Σ.

A realization of a finite set of events (hi i∈ I is a sequence of elements of {T, ⊥} I  \{ ⊥ I }.

either within any simply connected time interval, where are two consecutive switching points, or within any interval if the switching rule generates a finite sequence ST of switching time instants of last element.

In Definition 1, we say that X is π-connected if for any two elements x and y of X, there is a finite sequence ((x_{i})_{iin[0, l]_{mathbf{Z}}}) of elements in X such that (x=x_{0}), (y=x_{l}), and ((x_{j}, x_{j+1}) inpi ) for (j in[0, l-1]_{mathbf{Z}}).

The metric space ( S, d ) is ε-chainbale for some ε > 0 if for every x, y ∈ S, there exists a finite sequence ( x i ) n = 0 N of elements in S with x 0 = x, x N = y and d ( x i, x i + 1 ) < ε for i = 0, 1, …, N − 1. Remark 3.25 [12].

The PM space ( S, F ) is said to be -chainable if for each x, y ∈ S there exists a finite sequence ( x n ) n = 0 N of elements in S with x 0 = x and x N = y such that x i + 1 ∈ N x i for i = 0, 1, …, N − 1.