Definition:Axis

General Definition
An axis is the name used for a general infinite straight line which is particularly significant in some particular way in the study of linear transformations of a Real Vector Space.

Coordinate Axes
Consider a coordinate system.

One of the reference lines of such a system is called an axis.

The plural of axis is axes (pronounced "ax-eez" rather than "ax-iz" - compare basis).

X-Axis
In a cartesian coordinate system, the x-axis is the one usually depicted and visualised as going from left to right.

It consists of all the points in the Real Vector Space in question (usually either $$\R^2$$ or $$\R^3$$) at which all the elements of its coordinates but $$x$$ are zero.

Y-Axis
In a cartesian coordinate system, the y-axis is the one usually depicted and visualised as going from "bottom" to "top" of the paper (or screen).

It consists of all the points in the Real Vector Space in question (usually either $$\R^2$$ or $$\mathbb{R}^3$$) at which all the elements of its coordinates but $$y$$ are zero.