# Real Number Line and xy-Plane

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• Feb 11th 2019, 03:20 AM
harpazo
Real Number Line and xy-Plane
The real number line includes negative numbers, 0, and positive numbers. I also know that the x-axis and y-axis include the same. It is logical to say that the x-axis and y-axis are both real number lines that meet at the origin?
• Feb 11th 2019, 03:33 AM
HallsofIvy
Re: Real Number Line and xy-Plane
Yes, that is true. Even more, they form four right angles where they intersect and "right angles", or angles in general, cannot be defined in only one dimension. A Cartesian coordinate system, with x and y axes, can only be constructed in \$\displaystyle R^2\$ which is two dimensional.
• Feb 12th 2019, 05:25 AM
harpazo
Re: Real Number Line and xy-Plane
Quote:

Yes, that is true. Even more, they form four right angles where they intersect and "right angles", or angles in general, cannot be defined in only one dimension. A Cartesian coordinate system, with x and y axes, can only be constructed in \$\displaystyle R^2\$ which is two dimensional.

If R^2 = two dimensions, can we say that R^3 = three dimensions involving a third variable?
• Feb 12th 2019, 06:40 AM
Plato
Re: Real Number Line and xy-Plane
Quote:

If R^2 = two dimensions, can we say that R^3 = three dimensions involving a third variable?

Yes indeed.
\$\mathbb{R}^1\$ is the set of real numbers.
\$\mathbb{R}^2\$ is the set of pairs of real numbers.
\$\mathbb{R}^3\$ is the set of triples of real numbers.
• Feb 12th 2019, 07:27 AM
harpazo
Re: Real Number Line and xy-Plane
Quote:

Yes indeed.
\$\mathbb{R}^1\$ is the set of real numbers.
\$\mathbb{R}^2\$ is the set of pairs of real numbers.
\$\mathbb{R}^3\$ is the set of triples of real numbers.

Good to know in advanced. I plan to study Calculus 3 in the future. I always wanted to complete the calculus series.