eli5 What relationship does the Cartesian product R² and R³ have with the Cartesian plane and three-dimensional space?

Question

eli5 What relationship does the Cartesian product R² and R³ have with the Cartesian plane and three-dimensional space?

In: 2

Answer 1

R is the set of real numbers. It can also be represented by a number line.

If you pick a real number — call it x — you can plot it on the number line.

R² is 2 sets of real numbers. It’s the same set of real numbers, but twice.

You can pick a real number from each — call them x and y — and plot each one on its own corresponding number line.

OR you could rotate one of the number lines 90°, make it the Y axis to a Cartesian plane, and plot both x and y at once as a single point (x, y).

If you have N full sets of real numbers, you have a coordinate system in N-dimensional space.