Sentence examples for there exists a real number from inspiring English sources

Exact(59)

In general, there exists a real number R such that the series converges when −R < x < R but diverges if x < −R or x > R.

Due to the compactness of and boundness of, there exists a real number such that (3.1).

Otherwise, if, then there exists a real number such that when, which contradicts the condition that is integrable on.

If (Gsupset A), then there exists a real number (sigma>0) such that (Gsupset U sigma,A)).

where are constants, and satisfies the following hypothesis: is continuous, nondecreasing on, and nonincreasing on for each fixed there exists a real number such that for any, (1.3).

Since f is Δ-bounded there exists a real number A and (K_{2}= { tinmathbb{T}:vert f(t)vert leq A } ) with (delta_{Delta} ( K_{2} ) =1).

Then, since, there exists a real number such that (2.12).

if and only if there exists a real number with such that.

Since f is bounded, there exists a real number M such that supf(t) ≤ M.

Now we claim that there exists a real number r satisfying condition (2.2).

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Similar(1)

Then, and are called, (5) -subweakly commuting on (see [9]) if for all, there exists a real number such that, (6 uniformly -subweakly commuting on (see [10]) if there exists a real number such that, for all and.

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