A more useful example is the set of subsets of the real line formed by starting with all open intervals and adding in all countable unions, countable intersections, and relative complements and continuing this process until the relevant closure properties are achieved ( a construction known as the Borel σ-algebra Borel set ).

Venn diagram that shows the Intersection ( set theory ) | intersections of the Greek alphabet | Greek, ISO basic Latin alphabet | Latin and Russian alphabet | Russian alphabets ( Letter case | upper case letter ( alphabet ) | letter s )

* Line segment intersection: Find the intersections between a given set of line segments.

This set off a chain-reaction of sorts, with additional protesters pushing dumpsters into the middle of intersections and lighting them on fire, deflating the tires of police vehicles, non-black bloc demonstrators joining in the property destruction, and a general disruption of all commercial activity in downtown Seattle.

It is known that Ω ( X ) has certain special properties: it is a complete lattice within which suprema and infima of finite sets are given by set unions and finite set intersections, respectively.

The set of all topologies on a set X together with the partial ordering relation ⊆ forms a complete lattice that is also closed under arbitrary intersections.

# The collection of open sets consisting of all finite intersections of elements of B, together with the set X and the empty set, forms a basis for T. This means that every non-empty proper open set in T can be written as a union of finite intersections of elements of B.

By analogy, an étale presheaf is called a sheaf if it satisfies the same condition ( with intersections of open sets replaced by pullbacks of étale morphisms, and where a set of étale maps to U is said to cover U if the topological space underlying U is the union of their images ).

The structure of this set can be better understood by introducing a system of labels for all the intersections — a symbolic dynamics.

The team performs a program set to music, with required formations including circles, lines, blocks, wheels, and intersections.

On the American side, a number of state and national routes end at a set of intersections in front of the bridge.

The set of all subsets of X that are either countable or cocountable forms a σ-algebra, i. e., it is closed under the operations of countable unions, countable intersections, and complementation.

The intersection semilattice of A, written L ( A ), is the set of all subspaces that are obtained by intersecting some of the hyperplanes ; among these subspaces are S itself, all the individual hyperplanes, all intersections of pairs of hyperplanes, etc.

These are examples of an extremely important and powerful property of set algebra, namely, the principle of duality for sets, which asserts that for any true statement about sets, the dual statement obtained by interchanging unions and intersections, interchanging U and Ø and reversing inclusions is also true.

The following proposition states six more important laws of set algebra, involving unions and intersections.

It appears possible to set a lower limit of about Af for the activation energy of the abstraction of a chlorine atom from a carbon tetrachloride molecule by a chlorine atom to form Af radical.

When each number of successes X is paired with its probability of occurrence Af, the set of pairs Af, is a probability function called a binomial distribution.

This theorem is similar to the theorem of Kakutani that there exists a circumscribing cube around any closed, bounded convex set in Af.

In the C-plane we construct a set of rectangular Cartesian coordinates u, V with the origin at Q and such that both C and Af have finite slope at Q.

The fact that there can not be any limit points of the set except in closed intervals follows from the argument used in Lemma 1, namely, that near any tangent point in the C-plane the curves C and Af are analytic, and therefore the difference between them must be a monotone function in some neighborhood on either side of the tangent point.

I was at least conscious of the distinction in my full Yokuts presentation that awaits publication, in which, in listing ' Two-Stem Meanings ', I set off by asterisks those forms in which N of stem B was Af of stem A/3, the unasterisked ones standing for Af ; ;

or under ' Four Stems ', I set off by asterisks cases where the combined N of stems Af was Af.

The set of vectors Af constitutes the operating policy or, more briefly, the policy, and a policy is admissible if all the Af belong to S.

The words that end each line of the first stanza are used as line endings in each of the following stanzas, rotated in a set pattern.

The set rotated as well to present a different interview setting.

The Burt-McCollum sleeve valve, as used by the Scottish company Argyll for its cars, and later adopted by Bristol for its radial aircraft engines, used a single sleeve which rotated around a timing axle set at 90 degrees to the cylinder axle.

The only element that remained from the original set was the kitchen's left-hand wall and island which were rotated ninety degrees to become the back wall at the right of the kitchen, with some modification to the cosmetics.

The plate is then moved – either rotated by a set number of degrees or through 90 degrees according to preference – and then rocked in another pass.

The hurdy-gurdy's strings are similarly set into vibration by means of a " rosin wheel ," a wooden wheel which contacts the strings as it is rotated by means of a crank handle, creating a " bowed " tone.

Abu Rayhan Biruni ( b. 973 ) discussed the possibility of whether the Earth rotated about its own axis and around the Sun, but in his Masudic Canon, he set forth the principles that the Earth is at the center of the universe and that it has no motion of its own.

With the advent of auto-reverse ( playing the tape in both directions ), Nakamichi had long recognized that the angle of the tape passing over the playback head was not the same if the tape head was rotated in the opposite direction and its first approach was to track the azimuth on the tape itself by moving the head slightly-a very complex affair which led to the design of the Dragon with its NAAC, subsequently Nakamichi never revisited this approach and set its engineers in search of a more elegant solution.

A rotated square is drawn using two-point perspective, with each set of parallel lines leading to a different vanishing point.

Points can also be rotated using complex numbers, as the set of all such numbers, the complex plane, is geometrically a two dimensional plane.

At a slightly later time, the new basis in polar coordinates appears slightly rotated with respect to the first set.

A Kakeya needle set ( sometimes also known as a Kakeya set ) is a ( Besicovitch ) set within which a unit line segment can be rotated continuously through 180 degrees, returning to its original position with reversed orientation.

can be moved continuously from one to the other on a set of arbitrary small measure ), a set in which a unit line segment can be rotated continuously through 180 degrees can be created from a Besicovitch set consisting of Perron trees.

# The volume of a set might change when it is rotated

The data set may be rotated continuously into various planes to better appreciate the structure.

Then a set A with ap elements can be divided into a rings of length p, and the rings can be rotated separately.

Errors in construction resulted in a set of rebuilt sails that rotated clockwise.

The banding evident in the Rössler attractor is similar to a Cantor set rotated about its midpoint.

In some sports this is achieved without the need for half-time, for example in cricket, fielding positions of players are rotated after a set passage of play.