point

A point is that which has no part.

—Euclid

A point is the fundamental datum, representing a location on a field.

The location is specified by a collection of values, one value for each dimension of the field.

A plane as a two dimensional field contains points represented by two values.

These values are described as \((x, y)\) where values for \(x\) and \(y\) can be integers, rational, or algebraic.

Examples of valid points on a plane:

\[\begin{split}(0, 0)\\ (-3, \frac{8}{13})\\ (\frac{\sqrt{5}}{2}, 1)\end{split}\]