# Definition:Lattice Point

## Definition

Let $\CC$ be a cartesian coordinate system of $n$ dimensions.

Let $P = \tuple {a_1, a_2, \ldots, a_n}$ be a point in $\CC$.

Then $P$ is a lattice point of $\CC$ if and only if $a_1, a_2, \ldots, a_n$ are all integers.

### Rational Lattice Point

$P$ is a rational lattice point of $\CC$ if and only if $a_1, a_2, \ldots, a_n$ are all rational numbers.

## Also known as

A lattice point can also be referred to as an integral point.