n.
 (pl. identities)
    - the fact of being who or what a person or thing is. 
▸the characteristics determining this.
 ▸
[
as modifier]
 serving to establish the identity of the owner:
 an identity card.
 - a close similarity or affinity.
 - Mathematics  
(also identity operation)
 a transformation that leaves an object unchanged. 
▸
(also identity element)
 an element of a set which, if combined with another element, leaves that element unchanged.
 - Mathematics  an equation expressing the equality of two expressions for all values of the variables, e.g. (x + 1)2 = x2 + 2x + 1.
 
 
  Etymology
  C16: from late L. identitas, from L. idem ‘same’.