Sentence examples for and there exists from inspiring English sources

The phrase "and there exists" is correct and usable in written English.
It is typically used in mathematical or philosophical contexts to indicate the existence of at least one element that satisfies a certain condition.
Example: "In the realm of mathematics, it is often stated that for every positive integer n, there exists a prime number greater than n."
Alternatives: "and there is" or "and at least one exists".

Exact(60)

Device ageing is accelerated and there exists the risk of catastrophic failure by thermal runaway.

(B3) is continuous and there exists (3.4).

(C2 for any and, there exists satisfying.

Then and there exists such that (3.48).

By and, there exists such that (2.20).

and there exists, such that (3.2).

For and, there exists such that (3.44).

and there exists, where, such that (6.6).

Since and, there exists such that (4.8).

Then, for and, there exists such that (2.46).

If and, there exists an sufficiently small, such that (4.6).

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