This force is used in the formal definition of the ampere, which states that it is " the constant current that will produce an attractive force of 2 × 10 < sup >– 7 </ sup > newton per metre of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one metre apart in a vacuum ".

Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem.

While there is no generally accepted formal definition of " algorithm ," an informal definition could be " a set of rules that precisely defines a sequence of operations.

Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.

* Church, along with mathematician Stephen Kleene and logician J. B. Rosser created a formal definition of a class of functions whose values could be calculated by recursion.

By 1963 – 4 Gödel would disavow Herbrand – Gödel recursion and the λ-calculus in favor of the Turing machine as the definition of " algorithm " or " mechanical procedure " or " formal system ".

In a few years ( 1939 ) Turing would propose, like Church and Kleene before him, that his formal definition of mechanical computing agent was the correct one.

The formal definition of ' two natures ' in Christ was understood by the critics of the council at the time, and is understood by many historians and theologians today, to side with western and Antiochene Christology and to diverge from the teaching of Cyril of Alexandria, who always stressed that Christ is ' one '.

For example, in formal languages like mathematics, a ' stipulative ' definition guides a specific discussion.

Considerable controversy exists over the proper definition of the term " desertification " for which Helmut Geist ( 2005 ) has identified more than 100 formal definitions.

Then the equivalence class of the pair can be identified with the rational number, and this equivalence relation and its equivalence classes can be used to give a formal definition of the set of rational numbers.

This definition of potential, while formal, has little practical application, and a more useful concept is that of electric potential difference, and is the energy required to move a unit charge between two specified points.

Functional programming has its roots in lambda calculus, a formal system developed in the 1930s to investigate function definition, function application, and recursion.

While formal language theory usually concerns itself with formal languages that are described by some syntactical rules, the actual definition of the concept " formal language " is only as above: a ( possibly infinite ) set of finite-length strings, no more nor less.

By an abuse of the definition, a particular formal language is often thought of as being equipped with a formal grammar that describes it.

According to McBrien, the majority of the bishops were not so much interested in a formal definition of papal infallibility as they were in strengthening papal authority and, because of this, were willing to accept the agenda of the infallibilists.

Kasner decided to adopt a more formal definition " because different people get tired at different times and it would never do to have Carnera be a better mathematician than Dr. Einstein, simply because he had more endurance and could write for longer ".

The notion of a homomorphism can be given a formal definition in the context of universal algebra, a field which studies ideas common to all algebraic structures.

A new definition of hypnosis, derived from academic psychology, was provided in 2005, when the Society for Psychological Hypnosis, Division 30 of the American Psychological Association ( APA ), published the following formal definition:

Aristotle ( ca 350 BC ) was one of the first in recorded history to make a formal distinction between ordinary law and constitutional law, establishing ideas of constitution and constitutionalism, and attempting to classify different forms of constitutional government.

If a distinction is to be made between divination and fortune-telling, divination has a formal or ritual and often social character, usually in a religious context, as seen in traditional African medicine ; while fortune-telling is a more everyday practice for personal purposes.

) has been widely known in English by his Latinized name Gustavus Adolphus Magnus and variously in historical writings also as Gustavus, or Gustavus the Great, or Gustav Adolph the Great (, a formal distinction passed by the Swedish Parliament in 1634 ).

* Grammatical aspect represents a formal distinction encoded in the grammar of a language.

There is however no longer a formal distinction between an inn and other kinds of establishment.

There is no formal distinction between a lemma and a theorem, only one of intention – see Theorem # Terminology.

There is however no longer a formal distinction between an inn and other kinds of establishment.

*** Second person formal and informal pronouns ( T-V distinction ).

There is no distinction in modern English though Elizabethan English marked the distinction with " thou " ( singular informal ) and " you " ( plural or singular formal ).

The formal distinction between both fields is that physical chemistry is a branch of chemistry while chemical physics is a branch of physics.

This distinction has the status of a formal requirement in competitive walking events.

The distinction lies in the fact that the plus and minus signs on the amine oxide signify formal charges, not electrical charges.

There is no formal botanical distinction between bananas and plantains, and the use of either term is based purely on how the fruits are consumed.

However, the methods developed by Frege and Tarski for the study of mathematical language have been extended greatly by Tarski's student Richard Montague and other linguists working in formal semantics to show that the distinction between mathematical language and natural language may not be as great as it seems.

which is quite convenient, but one must be aware of the distinction between formal summation ( a mere convention ) and actual addition.

The points below illustrate the more formal usage, in terms of the distinction between emf and the voltage it generates:

In the fifth century, a formal distinction between anathema and " minor " excommunication evolved, where " minor " excommunication entailed cutting off a person or group from the rite of Eucharist and attendance at worship, while anathema meant a complete separation of the subject from the Church.

One other use of the distinction that occurs in some languages is the expression of " mock respect ", essentially a humorous way of expressing disapproval, by the use of the formal form to address people with whom one would not normally use it, such as children or close friends.

The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics ( in both senses of that term ).

This not only allowed new curves to be defined and studied, but it enabled a formal distinction to be made between curves that can be defined using algebraic equations, algebraic curves, and those that cannot, transcendental curves.

The formal distinction is that a gerund is a verbal noun – a noun derived from a verb that retains verb characteristics, that functions simultaneously as a noun and a verb, while other nouns in the form of the present participle ( ending in-ing ) are deverbal nouns, which function as common nouns, not as verbs at all.

With the compositional approach he took from the Third Symphony onward, Sibelius sought to overcome the distinction between symphony and tone poem to fuse their most basic principles — the symphony's traditional claims of weight, musical abstraction, gravitas and formal dialogue with seminal works of the past ; and the tone poem's structural innovation and spontaneity, identifiable poetic content and inventive sonority.

Some logicians ( Kenneth Ross, Charles Wright ) draw a firm distinction between the conditional connective ( the syntactic sign "→"), and the implication relation ( the formal object denoted by the double arrow symbol "⇒").