\begin{definition}[Definition:Equals]
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.
\end{definition}