Identically

Identically is an adverb meaning in the same way or in every respect; used to indicate exact sameness or equivalence between things. In general use, it can modify adjectives and verbs to stress that two or more items share the property described, as in "The two reports were identically formatted" or "The actions were identically performed." In some contexts it contrasts with merely similar or approximately so, signaling a precise correspondence.

In mathematics, identically refers to a property that holds for all permissible values of the variables. A statement that is true for all inputs is called an identity, and an expression may be said to be identically equal to another expression (often written with the symbol ≡). For example, sin^2 x + cos^2 x ≡ 1 for all x, or the derivative of e^x is identically e^x. A function that is identically zero satisfies f(x) = 0 for every x in its domain.

Origin and related terms: Identically derives from identic, via identity and identitas; etymology traces to Latin identicus from identitas and idem "the same." Related words include identical, identification, and identity. The adverb should not be confused with the adjective identical, which describes sameness of form or identity.