additive identity idâni-ye bardâyeši Fr.: identité additive The number which can be added to any other number without changing the magnitude of that number: zero. → multiplicative identity. |
entity hastâr (#) Fr.: entité 1) A real thing. From L.L. entitatem, from L.L. ens (genitive entis) "being, thing," from esse "to be," cognate with Pers. hast, ast, as below. Hastâr, from hast (noun), as in hast-o-nist, or contraction of hasti "existence," from hastan "to be" (variant astan, ast "is;" Mid.Pers. (h)ast "is," (h)astih "existence;" O.Pers. ah- "to be," astiy "is;" Av. ah- "to be" (ahmī, ahī, astī); cf. Skt. as- "to be," ásti "is;" Gk. esti "is;" L. est "is;" Russ. yest "is;" Goth. ist; E. is), + suffix -âr (as in padidâr). Alternatively, from hast (noun), as above, + -âr contraction of -dâr (as in dustâr) present stem of dâštan "to have, to possess" (Mid.Pers. dâštan, O.Pers./Av. root dar- "to hold, keep back, maintain, keep in mind," Skt. dhr-, dharma- "law," Gk. thronos "elevated seat, throne," L. firmus "firm, stable," Lith. daryti "to make," PIE *dher- "to hold, support"). |
identity idâni, inhamâni (#), kisti (#), cisti (#) Fr.: identité 1) Math.: An equation that is valid for all values of its variables.
A mathematical relationship equating one quantity to another. 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. |
identity axiom bondâšt-e idâni Fr.: axiome d'identité 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 element bonpâr-e idâni Fr.: élément neutre 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 function karyâ-ye idâni Fr.: fonction d'identité Math.: Any function f for which f(x) = x for all x in the domain of definition. |
identity matrix mâtris-e idâni Fr.: matrice identité In linear algebra, the simplest nontrivial diagonal matrix, an n-by-n square matrix with ones on the main diagonal and zeros elsewhere. |
identity operator âpârgar-e idâni Fr.: opérateur d'identité An operator which takes a real number to the same real number. |
law of identity qânun-e idâni Fr.: principe d'identité Same as → principle of identity. |
multiplicative identity idâni-ye bastâyeši Fr.: identité multiplicative The number which when used as the multiplier of another number leaves the second unchanged; one. → multiplicative; → identity. |
principle of identity parvaz-e idâni Fr.: principe d'identité 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. |