Sentence examples for exists a whole from inspiring English sources

Consider a sequence (an) of real numbers, by which is meant an infinite lista0, a1, a2, ….It is said that an converges to (or approaches) the limit a as n tends to infinity, if the following mathematical statement holds true: For every ε > 0, there exists a whole number N such that |an − a| < ε for all n > N.

Furthermore between nomadic and sedentary there exists a whole range of intermediary states whose boundaries are rarely clear.

For example, one may consider the idea that whenever there are some things, there exists a whole that consists exactly of those things i.e., that there is always a mereological sum (or "fusion") of two or more parts.

Having a set of nearly optimal system designs, for example, can be advantageous in many practical cases such as when there exists a whole set of optimal designs or in multi-objective optimization where there is a Pareto optimal set.

In view of (1.13), between hyponormality and subnormality there exists a whole slew of increasingly stricter conditions, each expressible in terms of the joint hyponormality of the tuples ((I,T,T ^{2},ldots,T^{k})).

This implies that there exists a whole manifold of fix-points related to each other via the symmetry transformation ((alpha_{s}, alpha_{i} to alpha_{s} e^{iphi}, alpha _{i} e^{-iphi})), where (alpha_{s}) and (alpha_{i}) are the rotating frame signal and idler mode amplitudes, respectively.

But his most extravagant assertion that there had existed a whole lost world, filled with lost species remained just that.

But his most extravagant assertion — that there had existed a whole lost world, filled with lost species — remained just that.

What if instead of using two dancing ballerinas to signify a Diane Arbus photo, there existed a whole realm of ready-made art emojis based off the cannon of art history?

My friend was alerting me to a secret order that existed, a whole community that employed thousands, that the government spent tens of millions on to subsidize, and that I, and many others, don't think twice about.

It encompasses not only outright denial that God exists, but a whole spectrum of self-assertion.