identity

noun (plural identities)

• 1the fact of being who or what a person or thing is:he knows the identity of the bombers [mass noun]:she believes she is the victim of mistaken identity
• the characteristics determining who or what a person or thing is:he wanted to develop a more distinctive Scottish Tory identity
• [as modifier] (of an object) serving to establish who the holder, owner, or wearer is by bearing their name and often other details such as a signature or photograph:an identity card

• 2a close similarity or affinity:an identity between the company’s own interests and those of the local community

• 3 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 by a specified binary operation, leaves that element unchanged.

• 4 Mathematics the equality of two expressions for all values of the quantities expressed by letters, or an equation expressing this, e.g. (x + 1)² = x² + 2x + 1.