Identity

Definition

An equality that is true for every permissible value of its variable or variables.

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Specification A3, A6 · Paper 1, Paper 2, Paper 3

An equality that is true for every permissible value of its variables; it is often written using $\equiv$ .
An identity states that two expressions have the same value for every permissible value of the variables.
Revise: Algebraic Vocabulary
An equality that is true for every permissible value of its variables.
Revise: Equations vs Identities

1
Checking several values can disprove an alleged identity if one fails, but successful checks alone do not prove that it is an identity.
2
First decide whether there is an equality sign. With no equality sign, the object is an expression rather than an equation or identity.
3
To justify an identity, simplify or expand one side until it becomes exactly the other side. Testing a few values is not a proof.

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Specification A3, A6 · Paper 1, Paper 2, Paper 3

An equality that is true for every permitted value of its variable or variables.
An identity is an equality that remains true for all permitted values of its variables.
Revise: Algebraic Vocabulary
Revise: Equations and Proof

Specification 6.01a · Paper 1 (Foundation), Paper 2 (Foundation), Paper 3 (Foundation), Paper 4 (Higher), Paper 5 (Higher), Paper 6 (Higher)

An equality that is true for every permitted value of its variable or variables, often written using $\equiv$ .
An identity is true for every permitted value of its variables.
Revise: Algebraic Proofs and Terms