Walter Crane

Walter Crane was a British artist and book illustrator. He is considered to be the most influential, among the most prolific, children's book creators of his generation and, along with Randolph Caldecott and Kate Greenaway, one of the strongest contributors to the child's nursery motif that the genre of English children's illustrated literature would exhibit in its developmental stages in the 19th century. Crane's work featured some of the more colourful and detailed beginnings of the child-in-the-garden motifs that would characterize many nursery rhymes and children's stories for decades to come, he was part of the Arts and Crafts movement and produced an array of paintings, children's books, ceramic tiles and other decorative arts. Crane is remembered for his creation of a number of iconic images associated with the international Socialist movement. Crane was the second son of Thomas Crane, a portrait painter and miniaturist, Marie Crane, the daughter of a prosperous malt-maker, his elder brother Thomas would go into illustration, sister Lucy was a noted writer.

He was a fluent follower of the newer art movements and he came to study and appreciate the detailed senses of the Pre-Raphaelite Brotherhood, was a diligent student of the renowned artist and critic John Ruskin. A set of coloured page designs to illustrate Tennyson's "Lady of Shalott" gained the approval of wood-engraver William James Linton to whom Walter Crane was apprenticed for three years in 1859–62; as a wood-engraver he had abundant opportunity for the minute study of the contemporary artists whose work passed through his hands, of Pre-Raphaelites Dante Gabriel Rossetti and John Everett Millais, as well as Sir John Tenniel, the illustrator of Alice in Wonderland, Frederick Sandys. He was a student who admired the masters of the Italian Renaissance, however he was more influenced by the Elgin marbles in the British Museum. A further and important element in the development of his talent was the study of Japanese colour-prints, the methods of which he imitated in a series of toy books, which started a new fashion.

From the early 1880s under William Morris's influence, Crane was associated with the Socialist movement. He did as much as Morris. With this object in view he devoted much attention to designs for textiles and wallpapers, to house decoration. For a long time he provided the weekly cartoons for the Socialist organs Justice, The Commonweal and The Clarion. Many of these were collected as Cartoons for the Cause, he devoted much time and energy to the work of the Art Workers Guild, of which he was master in 1888 and 1889 and to the Arts and Crafts Exhibition Society, which he helped to found in 1888. He was a Vice President of the Healthy and Artistic Dress Union, a movement begun in 1890, whose aim was to promote the loose-fitting clothing, in opposition to "stiffness and weight", they produced numerous pamphlets setting out their cause, including one entitled "How to Dress Without a Corset" which Crane illustrated. Although not himself an anarchist, Crane contributed to several libertarian publishers, including Liberty Press and Freedom Press.

He is credited with the design and decoration of the front facade of "The Bomb Shop", Henderson's bookshop at 66 Charing Cross Road specialising in left-wing and radical literature. Crane was controversial in his support of the four Chicago anarchists executed in 1887 in connection with the Haymarket affair. Visiting the United States for the first time in connection with an exhibition of his work in 1891, Crane scandalised polite society by appearing at a Boston anarchist meeting and expressing the opinion that the Haymarket defendants had been put to death wrongfully. Returning to his hotel, Crane found a letter stating that he faced "hopeless ruin" among American patrons of the arts owing to his support of those who were considered to be terrorist conspirators in public opinion of the day. Financial support was withdrawn and planned dinners in Crane's honour were cancelled. In response to the controversy, Crane wrote a letter to the press explaining that he had not meant to cause insult and did not himself favour the use of explosives, but had been expressing his principled opinion that those convicted were innocent of the crime for which they were charged.

The incident was memorialised in the press as "probably the most dramatic episode" in the artist's career. Walter Crane died on 14 March 1915 in West Sussex, his body was cremated at the Golders Green Crematorium. He was survived by three children, Beatrice and Lancelot. In 1862 his picture The Lady of Shalott was exhibited at the Royal Academy, but the Academy refused his maturer work and after the opening of the Grosvenor Gallery in 1877, he ceased to send pictures to Burlington House. In 1863 the printer Edmund Evans employed Crane to illustrate yellowbacks, in 1865 they began to collaborate on toy books of nursery rhymes and fairy tales. From 1865 to 1876 Crane and Evans produced two to three toy books each year; these are a few of his illustration suites: In 1864 he began to illustrate a series of sixpenny toy books of nursery rhymes in three colours for Edmund Evans. He was allowed more freedom in a series beginning with The Frog Prince which showed markedly the influence of Japanese art, of a long visit to Italy following on his marriage in 1871.

His work was characterized by sharp flat tints. The Baby's Opera was a book of English nursery songs available in 1877 with Evans, a third series of children's books with the collective title

Zermelo set theory

Zermelo set theory, as set out in an important paper in 1908 by Ernst Zermelo, is the ancestor of modern set theory. It bears certain differences from its descendants, which are not always understood, are misquoted; this article sets with the original text and original numbering. The axioms of Zermelo set theory are stated for objects, some of which are called sets, the remaining objects are urelements and do not contain any elements. Zermelo's language implicitly includes a membership relation ∈, an equality relation =, a unary predicate saying whether an object is a set. Versions of set theory assume that all objects are sets so there are no urelements and there is no need for the unary predicate. AXIOM I. Axiom of extensionality "If every element of a set M is an element of N and vice versa... M ≡ N. Briefly, every set is determined by its elements." AXIOM II. Axiom of elementary sets "There exists the null set, ∅, that contains no element at all. If a is any object of the domain, there exists a set containing only a as an element.

If a and b are any two objects of the domain, there always exists a set containing as elements a and b but no object x distinct from them both." See Axiom of pairs. AXIOM III. Axiom of separation "Whenever the propositional function – is definite for all elements of a set M, M possesses a subset M' containing as elements those elements x of M for which – is true." AXIOM IV. Axiom of the power set "To every set T there corresponds a set T', the power set of T, that contains as elements all subsets of T." AXIOM V. Axiom of the union "To every set T there corresponds a set ∪T, the union of T, that contains as elements all elements of the elements of T." AXIOM VI. Axiom of choice "If T is a set whose elements all are sets that are different from ∅ and mutually disjoint, its union ∪T includes at least one subset S1 having one and only one element in common with each element of T." AXIOM VII. Axiom of infinity "There exists in the domain at least one set Z that contains the null set as an element and is so constituted that to each of its elements a there corresponds a further element of the form, in other words, that with each of its elements a it contains the corresponding set as element."

The most used and accepted set theory is known as ZFC, which consists of Zermelo–Fraenkel set theory with the addition of the axiom of choice. The links show. There is no exact match for "elementary sets"; the empty set axiom is assumed by axiom of infinity, is now included as part of it. Zermelo set theory does not include the axioms of regularity; the axiom of replacement was first published in 1922 by Abraham Fraenkel and Thoralf Skolem, who had independently discovered that Zermelo's axioms cannot prove the existence of the set where Z0 is the set of natural numbers and Zn+1 is the power set of Zn. They both realized; the following year, John von Neumann pointed out that this axiom is necessary to build his theory of ordinals. The axiom of regularity was stated by von Neumann in 1925. In the modern ZFC system, the "propositional function" referred to in the axiom of separation is interpreted as "any property definable by a first-order formula with parameters", so the separation axiom is replaced by an axiom schema.

The notion of "first order formula" was not known in 1908 when Zermelo published his axiom system, he rejected this interpretation as being too restrictive. Zermelo set theory is taken to be a first-order theory with the separation axiom replaced by an axiom scheme with an axiom for each first-order formula, it can be considered as a theory in second-order logic, where now the separation axiom is just a single axiom. The second-order interpretation of Zermelo set theory is closer to Zermelo's own conception of it, is stronger than the first-order interpretation. In the usual cumulative hierarchy Vα of ZFC set theory, any one of the sets Vα for α a limit ordinal larger than the first infinite ordinal ω forms a model of Zermelo set theory. So the consistency of Zermelo set theory is a theorem of ZFC set theory. Zermelo's axioms do not imply the existence of ℵω or larger infinite cardinals, as the model Vω·2 does not contain such cardinals; the axiom of infinity is now modified to assert the existence of the first infinite von Neumann ordinal ω.

Zermelo's axioms cannot prove the existence of V ω as a set nor of any rank of the cumulative hierarchy of sets with infinite index. Zermelo allowed for the existence of urelements that are not contain no elements.

Mr. Big (Mr. Big album)

Mr. Big is the self-titled debut album by the American hard rock supergroup Mr. Big. Produced by Kevin Elson and Val Garay, the album proved a partial commercial success, reaching the 46th slot on the Billboard 200 chart. Lead-off single "Addicted to that Rush", featuring the band's aggressive guitar and bass playing brought the group some mainstream attention, reaching the No. 39 slot on the Billboard Mainstream Rock chart. 300,000 copies were sold, according to a Musician magazine interview with Mr. Big in 1990. Several of the songs from the album became live staples of the band, have since been included in various live albums; the group followed up the album with Lean Into It in 1991, which represented a critical breakthrough. The song "30 Days in the Hole" was recorded by British rock band Humble Pie on the 1972 album Smokin'. Bassist Billy Sheehan revealed on an interview on Nikki Sixx's radio show "Sixx Sense" that "Wind Me Up" is based on "Oh, Pretty Woman" by Roy Orbison played backwards.

Mr. BigEric Martin – lead vocals Paul Gilbert – guitar Billy Sheehan – bass guitar Pat Torpey – drumsProductionKevin Elson - producer, mixing Tom Size, Wally Buck - additional engineers Bob Ludwig - mastering at Masterdisk, New York Album - Billboard Singles - Billboard