An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

The number which can be added to any other number without changing the magnitude of that number: zero. → multiplicative identity.

→ additive; → identity.

1) Math.: An equation that is valid for all values of its variables. A mathematical relationship equating one quantity to another.
2) Logic: An assertion that two terms refer to the same thing.
3) Psychology: The character of persisting unchanged. The feeling that one knows who one really is.

From M.Fr. identité, from L.L. identitas "sameness," from ident-, combining form of L. idem "the same; at the same time; also; moreover," from id "it, that one" + demonstrative suffix -dem + -itas a suffix used to form abstract nouns expressing state or condition.

Idâni, from iduni, from Mid.Pers. êdônih "being this, being that, being so, the manner of being," from êdôn "thus, so," Mod.Pers. idun "this, in this manner, now;" O.Pers. aita- demonstrative pronoun "this;" Av. aēta- "this; this here; this now," aētaδ- (adv.) "here, there; then, thus; thereupon;" cf. Skt. etad "this," iti "thus, in this manner;" akin to L. idem, as above.

A basic rule in → group theory stating that there exists a unit group element e, called the identity, such that for any element a of the group a * e = e * a = a.

→ identity; → axiom.

In a mathematical system, an element which leaves unchanged any other element on which it operates. Thus 0 is the identity element for addition: a + 0 = a. And 1 is the identity element for multiplication: a . 1 = a.

→ identity; → element.

Math.: Any function f for which f(x) = x for all x in the domain of definition.

→ identity; → function.

In linear algebra, the simplest nontrivial diagonal matrix, an n-by-n square matrix with ones on the main diagonal and zeros elsewhere.

→ identity; → matrix.

An operator which takes a real number to the same real number.

→ identity; → operator.

Same as → principle of identity.

→ law; → identity.

The number which when used as the multiplier of another number leaves the second unchanged; one.

→ multiplicative; → identity.

The first principle of → formal logic introduced in Aristotle's theory of the → syllogism: If a statement is true then it is true. Also called → law of identity.

→ principle; → identity.