Links in this article to specific axioms of set theory describe some of the relationships between the informal discussion here and the formal axiomatization of set theory, but no attempt is made to justify every statement on such a basis.

The same is true of proofs, which are often expressed as logically organized and clearly worded informal arguments, intended to convince readers of the truth of the statement of the theorem beyond any doubt, and from which arguments a formal symbolic proof can in principle be constructed.

Nevertheless, theorems are usually expressed in natural language rather than in a completely symbolic form, with the intention that the reader will be able to produce a formal statement from the informal one.

This is sometimes supported by the statement that the whiskers of individual cats extend out to about the same width as the cat's body, but at least two informal reports indicate that whisker length is genetically determined and does not vary as the cat grows thinner or fatter.

Under Enriques it gradually became acceptable to use somewhat more informal arguments instead of complete rigorous proofs, such as the " principle of continuity " saying that what is true up to the limit is true at the limit, a claim that had neither a rigorous proof nor even a precise statement.

In October 2009, TAC issued a statement of Solidarity with Abahlali baseMjondolo condemning the attacks by ANC members on Kennedy Road informal settlement.

An informal geometric statement of the theorem is that for any positive integers n and c there is a number H such that if the cells of a H-dimensional n × n × n ×...× n cube are colored with c colors, there must be one row, column, diagonal etc.

In October 2009, War on Want issued a statement of solidarity with Abahlali baseMjondolo in response to the ANC affiliated attacks on the Kennedy Road informal settlement and wrote a letter to the South African High Commissioner in London.

Second, the condition that Taiwan accept any form of the one China principle is not explicitly mentioned in the text, and the statement that talks can occur in different modalities and in differing stages suggests that Beijing is willing to start at least informal talks without requiring a one China commitment.

( An informal definition of ) a clause in theorem proving is a statement that can result in a true or false answer depending on the evaluation of its literals.

" In his opening statement, Sen. Akaka stated, " organizations that help whistleblowers claim that OSC has gone from being their first option for relief to their last choice since OSC no longer works with agencies to achieve informal relief and the percentage of corrective actions and stays has been cut in half since 2002.

A user story is an informal statement of the requirement as long as the correspondence of acceptance testing procedures is lacking.

Apparently at the insistence of the U. S., the simultaneous announcements issued in Washington and Moscow last Friday emphasized the `` informal '' nature of the meeting.

On 1 September 2010, the Financial Crimes Enforcement Network issued an advisory on " informal value transfer systems " referencing United States v. Banki.

In England and Wales, injunctions whose existence and details may not be legally reported, in addition to facts or allegations which may not be disclosed, have been issued ; they have been given the informal name of superinjunctions ( or super-injunctions ).

On September 1, 2010, FinCEN issued an advisory on " informal value transfer systems " referencing United States v. Banki and Hawala.

Clearly today parliament tolerates only a very narrow exercise of the royal prerogative by issuance of letters patent, and such documents are issued with prior informal government approval, or indeed are now generated by government itself with the monarch's seal affixed as a mere formality.

In March 1985, the band issued the album The Power Station, produced by Bernard Edwards with some informal assistance from Nile Rodgers.

: a ) Warnings are informal warnings issued by police officers.

In 1567, Philip II of Spain issued a royal decree in Spain forbading Moriscos from use Arabic on all occasions, formal and informal, speaking and writing.

Occasionally an informal lesser advisory, known as " small craft exercise caution ," is issued for wind speeds lighter than those that call for a small craft advisory.

In 1567, Philip II of Spain issued a royal decree in Spain which forced Moriscos to abandon using Arabic on all occasions, formal and informal, speaking and writing.

Two days later, then-Attorney General of New York Eliot Spitzer, a supporter of same-sex marriage, issued an " informal opinion " stating that municipal clerks should not issue marriage licenses to same-sex couples since the New York State Legislature had not intended for the Domestic Relations Law to cover same-sex couples.

Shortly after Attorney General Spitzer's informal opinion was issued, five separate lawsuits were filed contesting the constitutionality of New York's opposite-sex definition of marriage.

Although the Mauritanian government has issued emancipation declarations, discrimination against Haratin is still widespread, and some continue to be, for all practical purposes, enslaved, while large numbers live in other forms of informal dependence on their former masters.

association by level of achievement is the dominant principle of informal relations.

In the basement the sheriff took him to a small, dingy office occupied by a tall, thin man informal in rolled-up shirt sleeves.

A trial de novo is usually available for review of informal proceedings conducted by some minor judicial tribunals in proceedings that do not provide all the procedural attributes of a formal judicial trial.

Gurevich: "... Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine ... according to Savage, an algorithm is a computational process defined by a Turing machine ".

These " conversations " as he called them, were more or less informal talks on a great range of topics, spiritual, aesthetic and practical, in which he emphasized the ideas of the school of American Transcendentalists led by Emerson, who was always his supporter and discreet admirer.

It has been argued that the name " Titus " in 2 Corinthians and Galatians is nothing more than an informal name used by Timothy, implied already by the fact that even though both are said to be long-term close companions of Paul, they never appear in common scenes.

In common law, black letter legal doctrine is an informal term indicating the basic principles of law generally accepted by the courts and / or embodied in the statutes of a particular jurisdiction.

Although trade unions in Benin represent up to 75 % of the formal workforce, the large informal economy has been noted by the International Trade Union Confederation ( ITCU ) to contain ongoing problems, including a lack of women's wage equality, the use of child labour, and the continuing issue of forced labour.

The history of baseball in the United States can be traced to the 18th century, when amateurs played a baseball-like game by their own informal rules using improvised equipment.

At that time, Olson and friend Rosalie ( Ricky ) Gaull Silberman started an informal network of women who supported the Thomas nomination to the Supreme Court despite allegations of sexual harassment by Anita Hill, a former subordinate of Thomas at the Equal Employment Opportunity Commission.

When the club folded after the 1870 season, Wright was hired by Boston businessman, Ivers Whitney Adams to organize a new team in Boston, and he did, bringing three teammates and the " Red Stockings " nickname along ( Most nicknames were then only nicknames, neither club names nor registered trademarks, so the migration was informal ).

Marie and Sudbury ), most retailers are prohibited from opening on Boxing Day, either by provincial law or municipal bylaw, or instead by informal agreement among major retailers in order to provide a day of relaxation following Christmas Day.

It can be done by systematically making explicit all the axioms, as in the case of the well-known book Naive Set Theory by Paul Halmos, which is actually a somewhat ( not all that ) informal presentation of the usual axiomatic Zermelo – Fraenkel set theory.

However, the term naive set theory is also used in some literature to refer to the set theories studied by Frege and Cantor, rather than to the informal counterparts of modern axiomatic set theory ; care is required to tell which sense is intended.

This is a feature of African American Vernacular English but is also used by a variety of English speakers in informal contexts.

However, no such text exists, apart from some informal popular lectures by Bohr and Heisenberg, which contradict each other on several important issues.

Before there was an official standard for C, many users and implementors relied on an informal specification contained in a book by Ritchie and Brian Kernighan ; that version is generally referred to as " K & R " C. In 1989 the American National Standards Institute published a standard for C ( generally called " ANSI C " or " C89 ").

The term clanking replicator was used by Drexler, is informal and is rarely used by others in popular or technical discussions.

To establish that a function is computable by Turing machine, it is usually considered sufficient to give an informal English description of how the function can be effectively computed, and then conclude " By the Church – Turing thesis " that the function is Turing computable ( equivalently partial recursive ).