Set definition (LaTeX command)

The colon and equal symbol (definition symbol) can be written by the coloneqq command and what it makes looks better than what the colon command makes as follows.

A \colon = \{ x \mid x^2 \lt 1 \} \\~\\
A \coloneqq \{ x \mid x^2 \lt 1 \}

\[ A \colon = \{ x \mid x^2 \lt 1 \} \\~\\ A \coloneqq \{ x \mid x^2 \lt 1 \} \]

Vertical bar

You can write a vertical bar by simply typing | but it's more common to use the mid command.

A \coloneqq \{ x | x^2 \lt 1 \} \\~\\
A \coloneqq \{ x \vert x^2 \lt 1 \} \\~\\
A \coloneqq \{ x \mid x^2 \lt 1 \} \\~\\
A \coloneqq \{ x \shortmid x^2 \lt 1 \}

\[ A \coloneqq \{ x | x^2 \lt 1 \} \\~\\ A \coloneqq \{ x \vert x^2 \lt 1 \} \\~\\ A \coloneqq \{ x \mid x^2 \lt 1 \} \\~\\ A \coloneqq \{ x \shortmid x^2 \lt 1 \} \]

Best solution

A \coloneqq \{ x \mid x^2 \lt 1 \}

\[ A \coloneqq \{ x \mid x^2 \lt 1 \} \]