$$

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 $a⟹b$ as “$a$ implies $b$”.

Biconditional

See: wikipedia on biconditional.

Read $a⟺b$ as “$a$ if and only if $b$”.

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.

Vectors

Read $\overrightarrow{v}$ as “vector v”.

See Vectors and dot products.

End of proof

Read $◼$ as “This completes the proof”.