\(\newcommand{L}[1]{\| #1 \|}\newcommand{VL}[1]{\L{ \vec{#1} }}\newcommand{R}[1]{\operatorname{Re}\,(#1)}\newcommand{I}[1]{\operatorname{Im}\, (#1)}\)

# Notation¶

## Defined as¶

\(\triangleq\) means “is defined as”. For example, read:

\[i \triangleq \sqrt{-1}\]

as “\(i\) is defined as the square root of -1.”

## Implies¶

Read \(a \implies b\) as “\(a\) implies \(b\)”.

## Set membership¶

\(\in\) means “in” or “one of”. For example:

\[k \in 0, 2, 4\]

means that the value \(k\) can take any of the three values 0, 2 or 4.

\(\notin\) means “not in” or “not one of”. For example:

\[k \notin 1, 3, 5\]

means that the value \(k\) can *not* take any of the three values 1, 3 or
5, but, all other things being equal, can take any other value.

## End of proof¶

Read \(\blacksquare\) as “This completes the proof”.