There are pairs of degrees with no greatest lower bound.

The infimum is a greatest lower bound or meet of a set.

Every pair of concepts in this partial order has a unique greatest lower bound (meet).

Any two elements have a greatest lower bound.

Greatest lower bounds in turn are given by the greatest common divisor.

In this context, especially in lattice theory, greatest lower bounds are also called meets.

Non-deterministic choice between programs is their greatest lower bound:

In other words, is the infimum (greatest lower bound) of the function .

So the outer/superior limit is the greatest lower bound on this sequence of joins of tails.

The greatest lower bound of any family of substructures is their interesction.

Now proceed to the node holding the greatest lower bound for the node that the new value was inserted to.

The dual concept of supremum, the greatest lower bound, is called infimum and is also known as meet.

Replacing "greatest lower bound" with "least upper bound" results in the dual concept of a join-semilattice.

Infimum (greatest lower bound)

Least upper bounds (suprema, ) and greatest lower bounds (infima, )

In this case the products and coproducts correspond to greatest lower bounds (meets) and least upper bounds (joins).

The "Infimum" or "Greatest Lower Bound" of the set of numbers 2, 3, 4 is 2.

Recall that a lattice is a partially ordered set in which any two elements and have a least upper bound and a greatest lower bound .

For example, in lattice theory, one is interested in orders where all finite non-empty sets have both a least upper bound and a greatest lower bound.

When ordering by set inclusion, the infimum limit is the greatest lower bound on the set of accumulation points because it is contained in each of them.

If the node's data array now has less than the minimum number of elements then move the greatest lower bound value of this node to its data value.

(If "K" contained a positive infinitesimal it would be a lower bound for the set whence zero would not be the greatest lower bound.)

Dually, a meet-semilattice (or lower semilattice) is a partially ordered set which has a meet (or greatest lower bound) for any nonempty finite subset.

A meet on a set is defined as the unique infimum (greatest lower bound) with respect to a partial order on the set, provided an infimum exists.

In the study of complete lattices, the join and meet operations are extended to return the least upper bound and greatest lower bound of an arbitrary set of elements.