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

Well you can have collections of 2 numbers as well as 3. You can represent the collection of 1 numbers on a line. Now for R² it can be represented on a plane. Pick every R² has a position on a plain. Now same with R³ but add another axis. Every element of R³ can be represented as a point in 3D space.