empty set

In particular, the empty set and the whole space are closed.

A player who cannot move because the choice is from the empty set has lost.

Although the empty set has no members, it can be a member of other sets.

Therefore, the empty set is the only partition of itself.

The only closed sets are the empty set and X.

Thus, the empty set is abstract because it cannot act on other objects.

Here the maximum of the empty set is taken to be zero.

A set with no members is called an empty set.

If it returns false, we immediately return the empty set.

The empty set is an identity element for the operation of union.

Note that the empty set is a face of every simplex.

An empty setting stared up at me like a blind eye.

An intersection of flats is either a flat or the empty set.

When a is less than 0, M is the empty set.

But for the empty set the statement may very well reduce to a vacuous truth.

The number of ways to choose 0 elements from the empty set is .

We have that each set is finite or the empty set.

By definition, this is the least element among all elements that are greater than each member of the empty set.

Thus we can talk of the (unique) empty set.

Many possible properties of sets are trivially true for the empty set.

In this context, zero is modelled by the empty set.

In contrast to a ball, a sphere may be an empty set, even for a large radius.

A and B are disjoint if their intersection is the empty set.

Some authors include the empty set in this definition.

The camera zooms out to reveal that the room is an otherwise empty set.