# Thread: Real Number Line and xy-Plane

1. ## 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?

2. ## 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.

3. ## Re: Real Number Line and xy-Plane

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?

4. ## Re: Real Number Line and xy-Plane

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.

5. ## Re: Real Number Line and xy-Plane

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.