Sentence examples for if exists for from inspiring English sources

The function is called -differentiable on if exists for all.

Moreover, is said to be delta or Hilger differentiable on if exists for all.

The space is said to be smooth if exists for all, where denotes the unit sphere of.

A minimalizing mapping has a fixed point if every nonempty chain has the infimum in, and if exists for all.

If nonempty chains of have supremums, and if exists for all, then exists, and is a fixed point of.

(c) If nonempty chains of have supremums, and if exists for all, then exists, and is a fixed point of  .

While there is a lot of debate regarding where that place exists (or if it exists, or if anything exists for that matter), it can be said with absolute certainty that DMT Town looks very cool.

In his will, Tudor stipulated that a dance score be used, if one exists, for any future stagings in order to ensure the integrity of his ballets.

If, then exists, for all.

(ii) We say that ρ satisfies (UUC1) if there exists, for every, and such that  .

The order p is the minimal number (if it exists) for which the decomposition (4) holds.