Sentence examples for given there exist from inspiring English sources

For given there exist the sequences and such that (4.13).

Suppose that for any given there exist subintervals and of such that (32).

By the compactness of, for any given, there exist such that and.

Suppose that for any given, there exist intervals, for which (a - b) hold.

Given, there exist a constant and a sequence of increasing positive numbers such that and (3.6).

Similarly, by choosing parameter, for any given, there exist function, function, and such that (518).

Given, there exists such that (3.19)  .

For given there exists a such that (3.6).

Since is continuous, then, given, there exists such that.

Then, given, there exists, and satisfying such that (3.15).

For any given, there exists a subsequence such that.