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

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

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Anonymous 0 Comments

You can think of them as the same thing.

R^2 is the set of all pairs of real numbers. The plane
Is a way to visualize the set geometrically as a space, where a pair of real numbers are coordinates.

Same with R^3. It’s the set of all triples of real numbers, which can be visualized as coordinates in 3d space

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