✎ Symbols [The Physics Travel Guide]

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====== Symbols ======

\begin{align}
&\mathbb{N} = \{0, 1, 2, 3, \ldots\} \\
&\mathbb{Z} = \{0, \pm 1, \pm 2, \pm 3, \ldots \} \\
&\mathbb{Q} = \rm Rational \; Numbers \it \\
&\mathbb{R} = \rm Real \; Numbers \it \\
&\mathbb{C} = \rm Complex \; Numbers \it \\
&\mathbb{Z}_n = \mathbb{Z} \; \mod \; n \\
&\Rightarrow \rm \; is \; read \; ``implies"\\
&\rm iff \; is \; read \; ``if\; and \; only \; if" \\
&\forall  \rm \; is \; read \; ``for \; every" \\
&\exists  \rm \; is \; read \; ``there \; exists" \\
&\in \;  \rm is \; read \; ``in" \\
&\ni \;   \rm is \; read \; ``such \; that" \\
&\dot{=} \; \rm is \; ``represented \; by" \\
&\subset \; \rm is \; ``subset\; of" \\
&\equiv \; \rm is\;``defined\; as" \\
\end{align}

There are several species of equality:
\begin{align}
= & \quad \text{exactly equal} \notag \\
\propto & \quad \text{equality except perhaps for a factor with dimension} \notag\\
\sim & \quad \text{equality except perhaps for a factor without dimensions} \notag \\
\approx & \quad  \text{equality except perhaps for a factor close to 1}
\end{align}

Source: page 6 in Street Fighting Mathematics by Mahajan

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