# Real Number Line and xy-Plane

• 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:

Originally Posted by HallsofIvy
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:

Originally Posted by harpazo
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:

Originally Posted by Plato
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.