identity,
n. 1. also called numerical identity. the property or fact of being the same individual. For example, one speaks of the identity of a1/2 and √a.
2. (Logic) the relation that trivially holds between every entity and itself, formally defined as the set of ordered pairs 〈x, x〉 for all x in the underlying domain.
3. a universally true equation, one that is not to be solved for the value of its variables that makes it true, but that is true for all values of its variables. For example, in
(x + y)(x - y) = x2- y2,
or trigonometric identities such as
sin2 θ + cos2 θ = 1.
Identities are sometimes written using the `≡' sign. 4. see identity element.
5a. also called qualitative identity. the property of being exactly alike, or the relation that holds between such entities. For example, the identity of congruent triangles can be shown by superimposition.
b. see relative identity. 6. (Logic) an assertion that the relation of identity holds, such as `ex is expx'; any statement of which the operator of widest scope is `='.
(x + y)(x - y) = x2- y2,
or trigonometric identities such as
sin2 θ + cos2 θ = 1.
Identities are sometimes written using the `≡' sign. 4. see identity element.
5a. also called qualitative identity. the property of being exactly alike, or the relation that holds between such entities. For example, the identity of congruent triangles can be shown by superimposition.
b. see relative identity. 6. (Logic) an assertion that the relation of identity holds, such as `ex is expx'; any statement of which the operator of widest scope is `='.