Definition:Equals

Definition
The symbol $=$ means equals.
 * $x = y$ means $x$ is the same object as $y$, and is read $x$ equals $y$, or $x$ is equal to $y$.


 * $x \ne y$ means $x$ is not the same object as $y$, and is read $x$ is not equal to $y$.

The expression:
 * $a = b$

means:
 * $a$ and $b$ are names for the same object.

Equality
The word equality is the noun derived from the verb equals.

Note on Terminology
Two objects being equal is not necessarily the same as two objects being congruent.

This distinction is often not made.

When such a difference is important the symbol $=$ may be used for equals and $\cong$ for congruent.

Also see

 * Equality is Equivalence Relation
 * Axiom:Leibniz's Law
 * Definition:Diagonal Relation
 * Definition:Set Equality