Addition

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic, with the others being subtraction, multiplication and division. The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" i.e., "3 add 2 is equal to 5".

Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.

In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.

Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.

Disjunction introduction

Disjunction introduction or addition (also called or introduction) is a simple valid argument form, an immediate inference and a rule of inference of propositional logic. The rule makes it possible to introduce disjunctions to logical proofs. It is the inference that if P is true, then P or Q must be true.

The rule can be expressed as:

where the rule is that whenever instances of "" appear on lines of a proof, "" can be placed on a subsequent line.

Disjunction introduction is controversial in paraconsistent logic because in combination with other rules of logic, it leads to explosion (i.e. everything becomes provable). See Tradeoffs in Paraconsistent logic.

Formal notation

The disjunction introduction rule may be written in sequent notation:

where is a metalogical symbol meaning that is a syntactic consequence of in some logical system;

and expressed as a truth-functional tautology or theorem of propositional logic:

where and are propositions expressed in some formal system.

Addition (disambiguation)

Addition is the mathematical process of putting things together.

Addition may also refer to:

Ataxia

Ataxia (from Greek α- [a negative prefix] + -τάξις [order] = "lack of order") is a neurological sign consisting of lack of voluntary coordination of muscle movements that includes gait abnormality. Ataxia is a non-specific clinical manifestation implying dysfunction of the parts of the nervous system that coordinate movement, such as the cerebellum. Ataxia can be limited to one side of the body, which is referred to as hemiataxia. Several possible causes exist for these patterns of neurological dysfunction. Dystaxia is a mild degree of ataxia. Friedrich's ataxia has gait abnormality as the most commonly presented symptom.

Types

Cerebellar

The term cerebellar ataxia is used to indicate ataxia that is due to dysfunction of the cerebellum. The cerebellum is responsible for integrating a significant amount of neural information that is used to coordinate smoothly ongoing movements and to participate in motor planning. Although ataxia is not present with all cerebellar lesions, many conditions affecting the cerebellum do produce ataxia. People with cerebellar ataxia may have trouble regulating the force, range, direction, velocity and rhythm of muscle contractions. This results in a characteristic type of irregular, uncoordinated movement that can manifest itself in many possible ways, such as asthenia, asynergy, delayed reaction time, and dyschronometria. Individuals with cerebellar ataxia could also display instability of gait, difficulty with eye movements, dysarthria, dysphagia, hypotonia, dysmetria and dysdiadochokinesia. These deficits can vary depending on which cerebellar structures have been damaged, and whether the lesion is bilateral or unilateral.

Ataxia (disambiguation)

Ataxia is a neurological sign consisting of lack of voluntary coordination of muscle movements that includes gait abnormality.

Ataxia may also refer to:

Ataxia (genus)

Ataxia, described by Haldeman in 1847, is an American genus of longhorn beetles of the subfamily Lamiinae, tribe Pteropliini.

Distribution

Ataxia is primarily widespread in South America, but several endemic species are present in Central America and in the Antilles. Only few species reach the South-western USA.

The genus includes 38 species: