If all chains have a supremum, the order is called chain complete.

When considering the whole flows, the supremum of these values is used.

Therefore, there exists a such that the supremum is finite.

Consider the sequence where the supremum is taken over all .

Its development of the real numbers relies on the supremum axiom.

Likewise the supremum on any particular subinterval is given by its end point.

If the supremum of a subset S exists, it is unique.

This set has a supremum but no greatest element.

However, if an infimum or supremum does exist, it is unique.

Hence, it is the supremum of the limit points.

For a set, they are the infimum and supremum of the set's limit points, respectively.

Find a sequence so that its image converges to the supremum of f.

A similar result is derived concerning the supremum norm.

Finding a supremum means to single out one distinguished least element from the set of upper bounds.

The definition of as a supremum then gives .

The infimum is in a precise sense dual to the concept of a supremum.

It is the infimum of the empty set and the supremum of P.

If the supremum belongs to the set, then it is the greatest element in the set.

Put more directly, it is the supremum of the set of smaller ordinals.

The space Y should also be an ordered set, so that the notions of supremum and infimum make sense.

Since D is compact, this supremum is actually attained by a set of points.

Use continuity to show that the image of the subsequence converges to the supremum.

Corimbion supremum is a species of beetle in the family Cerambycidae.

Suppose that is the supremum of the diameters of such balls.

The number is the supremum of the set of epsilon numbers .