Russell's Attic - Definition. Was ist Russell's Attic
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Was (wer) ist Russell's Attic - definition

UPPER PART OF A CONSTRUCTION, PLACED ABOVE AN ENTABLATURE OR CORNICE
Attic Style; Attique; Attic storey; Attic Order; Attic style
  • Attic

Russell's Attic      
<mathematics> An imaginary room containing countably many pairs of shoes (i.e. a pair for each natural number), and countably many pairs of socks. How many shoes are there? Answer: countably many (map the left shoes to even numbers and the right shoes to odd numbers, say). How many socks are there? Also countably many, we want to say, but we can't prove it without the Axiom of Choice, because in each pair, the socks are indistinguishable (there's no such thing as a left sock). Although for any single pair it is easy to select one, we cannot specify a general method for doing this. (1995-03-29)
Russell's Paradox         
PARADOX IN SET THEORY CONCERING THE SET OF ALL SETS NOT CONTAINING THEMSELVES
Russells Paradox; List of all lists which do not contain themselves; Russell's Paradox; Russell set; Russel's paradox; Paradosso di Russell; Russell paradox; Russell's antinomy; Bertrand Russell Paradox; Russels paradox; Russell's antinome; Russel paradox; Russell antinomy; Set of all sets that do not contain themselves; The set of all sets that do not contain themselves; Set of sets that do not contain themselves; Set of sets that don't contain themselves; Russell's antinomie; Russell’s paradox; Principle of comprehension; User:Lulu of the Lotus-Eaters/List of every Wikipedia list that does not contain itself; Russells paradox; Russell Paradox; Russells' Paradox; Russells's Paradox; Does the set of all sets contain itself?; Does the set of all sets contain itself; List of lists that don't include themselves
<mathematics> A logical contradiction in set theory discovered by Bertrand Russell. If R is the set of all sets which don't contain themselves, does R contain itself? If it does then it doesn't and vice versa. The paradox stems from the acceptance of the following axiom: If P(x) is a property then x : P is a set. This is the Axiom of Comprehension (actually an axiom schema). By applying it in the case where P is the property "x is not an element of x", we generate the paradox, i.e. something clearly false. Thus any theory built on this axiom must be inconsistent. In lambda-calculus Russell's Paradox can be formulated by representing each set by its characteristic function - the property which is true for members and false for non-members. The set R becomes a function r which is the negation of its argument applied to itself: r = x . not (x x) If we now apply r to itself, r r = ( x . not (x x)) ( x . not (x x)) = not (( x . not (x x))( x . not (x x))) = not (r r) So if (r r) is true then it is false and vice versa. An alternative formulation is: "if the barber of Seville is a man who shaves all men in Seville who don't shave themselves, and only those men, who shaves the barber?" This can be taken simply as a proof that no such barber can exist whereas seemingly obvious axioms of set theory suggest the existence of the paradoxical set R. Zermelo Frankel set theory is one "solution" to this paradox. Another, type theory, restricts sets to contain only elements of a single type, (e.g. integers or sets of integers) and no type is allowed to refer to itself so no set can contain itself. A message from Russell induced Frege to put a note in his life's work, just before it went to press, to the effect that he now knew it was inconsistent but he hoped it would be useful anyway. (2000-11-01)
Russell's paradox         
PARADOX IN SET THEORY CONCERING THE SET OF ALL SETS NOT CONTAINING THEMSELVES
Russells Paradox; List of all lists which do not contain themselves; Russell's Paradox; Russell set; Russel's paradox; Paradosso di Russell; Russell paradox; Russell's antinomy; Bertrand Russell Paradox; Russels paradox; Russell's antinome; Russel paradox; Russell antinomy; Set of all sets that do not contain themselves; The set of all sets that do not contain themselves; Set of sets that do not contain themselves; Set of sets that don't contain themselves; Russell's antinomie; Russell’s paradox; Principle of comprehension; User:Lulu of the Lotus-Eaters/List of every Wikipedia list that does not contain itself; Russells paradox; Russell Paradox; Russells' Paradox; Russells's Paradox; Does the set of all sets contain itself?; Does the set of all sets contain itself; List of lists that don't include themselves
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox discovered by the British philosopher and mathematician Bertrand Russell in 1901.Russell, Bertrand, "Correspondence with Frege}.

Wikipedia

Attic (architecture)

In classical architecture, the term attic refers to a storey (or low wall) above the cornice of a classical façade. The decoration of the topmost part of a building was particularly important in ancient Greek architecture and this came to be seen as typifying the Attica style, the earliest example known being that of the monument of Thrasyllus in Athens.

It was largely employed in Ancient Rome, where their triumphal arches utilized it for inscriptions or for bas-relief sculpture. It was used also to increase the height of enclosure walls such as those of the Forum of Nerva. By the Italian revivalists it was utilized as a complete storey, pierced with windows, as found in Andrea Palladio's work in Vicenza and in Greenwich Hospital, London. One well-known large attic surmounts the entablature of St. Peter's Basilica, which measures 12 metres (39 ft) in height.

Decorated attics with pinnacles are often associated with the Late Renaissance (Mannerist architecture) period in Poland and are viewed as a distinct feature of Polish historical architecture (attyka polska). Many examples can be found throughout the country, notably at Wawel Castle in Kraków, Gdańsk, Poznań, Lublin, Tarnów, Zamość, Sandomierz and Kazimierz Dolny. Possibly the best example of a rich Italianate attic is at Krasiczyn Castle.

This usage became current in the 17th century from the use of Attica style pilasters as adornments on the top story's façade. By the 18th century this meaning had been transferred to the space behind the wall of the highest story (i.e., directly under the roof), producing the modern meaning of the word "attic".