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In many cases, only lower and upper bounds are known with a large gap between them.

This is an immediate consequence of the upper bounds described below.

Even if a set has some upper bounds, it need not have a greatest element, as shown by the example of the negative real numbers.

In this way, both the lower and upper bounds are programmable.

The first upper bounds were based on the 'human' algorithms.

A set S is bounded if it has both upper and lower bounds.

There is now a clear strategy for finding lower and upper bounds for a 'good' exposure.

This can now be chosen in some arbitrary manner as a point between the lower and upper bounds.

It may help to point out that the increasing sequences produced by sequential programs all have least upper bounds.

The Levenshtein distance has several simple upper and lower bounds.