: For any set A, the power set of A ( with the empty set removed ) has a choice function.

Its domain is the powerset of A ( with the empty set removed ), and so makes sense for any set A, whereas with the definition used elsewhere in this article, the domain of a choice function on a collection of sets is that collection, and so only makes sense for sets of sets.

Miller sent a boat under Lieutenant William Hoste to take possession of the empty vessel, but Standelet had set fire to his ship as he left and Artémise blew up shortly afterwards.

We also allow for an empty set, often denoted Ø and sometimes: a set without any members at all.

Since a set is determined completely by its elements, there can only be one empty set.

( See axiom of empty set.

These categories surely have some objects that are " special " in a certain way, such as the empty set or the product of two topologies, yet in the definition of a category, objects are considered to be atomic, i. e., we do not know whether an object A is a set, a topology, or any other abstract concept – hence, the challenge is to define special objects without referring to the internal structure of those objects.

But how can we define the empty set without referring to elements, or the product topology without referring to open sets?

* Any finite topological space, including the empty set, is compact.

# The empty set and the whole vector-space are convex.

If one set is used, pieces race across the field into empty, opposite corners.

In keeping with the concept of vacuous truth, when disjunction is defined as an operator or function of arbitrary arity, the empty disjunction ( OR-ing over an empty set of operands ) is often defined as having the result 0.

There was another game where little puppets and dolls dressed as western foreigners with blue eyes ( Iranian peoples ) were set up and when one fell over, the person it pointed to had to empty his cup of wine.

The intersection of any two different cells is empty ; the union of all the cells equals the original set.

* The empty relation R on a non-empty set X ( i. e. aRb is never true ) is vacuously symmetric and transitive, but not reflexive.

The empty set is the set containing no elements.

In mathematics, and more specifically set theory, the empty set is the unique set having no elements ; its size or cardinality ( count of elements in a set ) is zero.

`` This is a mighty empty country '', Morgan said.

The `` reality '' to which they respond is rationally empty and their art is an imitation of the inescapable powerfulness of this unknown and empty world.

F.S.C. Northrop, in his discussion of The `` Functions And Future Of Poetry '', suggests this: `` One of the things which makes our lives drab and empty and which leaves us, at the end of the day, fatigued and deflated spiritually is the pressure of the taxing, practical, utilitarian concern of common-sense objects.

It is no coincidence that the hebephrenic patient, the most severely dedifferentiated of all schizophrenic patients, shows, as one of his characteristic symptoms, laughter -- laughter which now makes one feel scorned or hated, which now makes one feel like weeping, or which now gives one a glimpse of the bleak and empty expanse of man's despair ; ;

It is as empty as the word `` Hurrah '' would be when there was no enthusiasm behind it.

One is led to speculate as to why the empty space was there, left for our century to finish.

You may ask what else there is, and the answer is nothing -- nothing but empty space.

How Maxwell recounts his first coming to Camusfearna, his furnishing the empty house with beach-drift, the subtle changes in season over ten years, is a moving experience.

This room is currently empty.

You may continue to replace unplayable tiles ( including new unplayable tiles that you draw ) until you have six playable tiles or the tile stock is empty.

A big disadvantage of complex biological sewage treatment systems is that if the house is empty, the sewage system biota may starve to death.

( 1 is given by the empty product.

The Big Bang is not an explosion of matter moving outward to fill an empty universe.

From empty in chapter 1, she is filled again by God at the end of chapter 4.

Another closely related explanation is that reality is devoid of sensory mediation and conception, or empty, and therefore language itself is a priori inadequate without direct experience.

a − λ1 is not invertible ( because the spectrum of a is not empty ) hence a = λ1: this algebra A is naturally isomorphic to C ( the complex case of the Gelfand-Mazur theorem ).

For four or more points on the same circle ( e. g., the vertices of a rectangle ) the Delaunay triangulation is not unique: each of the two possible triangulations that split the quadrangle into two triangles satisfies the " Delaunay condition ", i. e., the requirement that the circumcircles of all triangles have empty interiors.

* Similarly, the empty space is the unique initial object in the category of topological spaces ; every one-point space is a terminal object in this category.

* In the category Rel of sets and relations, the empty set is the unique zero object.

* In the category of semigroups, the empty semigroup is the unique initial object and any singleton semigroup is a terminal object.

Terminal objects in a category C may also be defined as limits of the unique empty diagram ∅ → C. Since the empty category is vacuously a discrete category, a terminal object can be thought of as an empty product ( a product is indeed the limit of the discrete diagram

Formally, a unique factorization domain is defined to be an integral domain R in which every non-zero and non-unit x of R can be written as a product ( including an empty product ) of irreducible elements p < sub > i </ sub > of R and a unit u:

395 ( 1998 ) ( empty, torn, knotted piece of baggie, in plain view, gave officer probable cause to search car because baggie was a unique container, officer had previous experience with such containers, and stop occurred in area known for drug transactions ).

To-day these harbours are empty and idle solely because English policy is determined to retain Ireland as a barren bulwark for English aggrandisement, and the unique geographical position of this island, far from being a benefit and safeguard to Europe and America, is subjected to the purposes of England's policy of world domination.

Even in death he was unique — due to overwhelming popular request there were three funeral services: the first in Rome, a second in his birth city Naples — and a few days later, in a third one by the local Camorra boss, an empty casket was carried along the packed streets of the popular Rione Sanità quarter where he was born.

Some grammarians object to the use of the superlative or comparative with words such as full, complete, unique, or empty, which by definition already denote either a totality, an absence, or an absolute.

This type of usage conveys more of a figurative than a literal meaning, since in a strictly literal sense, something cannot be more or less unique or empty to a greater or lesser degree.

The empty subset is a valid graph since for every x in the domain ∅ there is a unique y in the codomain A such that.

The existence of a unique empty function from ∅ into each set A means that the empty set is an initial object in the category of sets.

Here C is either empty or Prikry generic over K ( so it has order type ω and is cofinal in κ ) and unique except up to a finite initial segment.

* Collinson's Cafe an unusual building which is currently empty with several unique architectural features including a rotunda and large sprung dancefloor from its time as a dancehall ; it can be found above the promenade on the road leading to the golf course

The identity element is the unique sequence of zero elements, often called the empty string and denoted by ε or λ, and the monoid operation is string concatenation.

The unique symbol from the generating set corresponds to natural number 1, the empty sequence to natural number 0, and every natural number n to the sequence where the unique symbol from the generating set appears exactly n-times.

Young tableaux can be identified with skew tableaux in which is the empty partition ( 0 ) ( the unique partition of 0 ).

A dabbawala (); also spelled as dabbawalla or dabbawallah ; literally meaning (" box person "), is a person in India, most commonly found in the city of Mumbai, who is employed in a unique service industry whose primary business is collecting freshly cooked food in lunch boxes from the residences of the office workers ( mostly in the suburbs ), delivering it to their respective workplaces and returning the empty boxes back to the customer's residence by using various modes of transport.