# What does (x,y) mean?

Aug 10, 2018

See explanation below

#### Explanation:

$\left(x , y\right)$ is a pair of real numbers. The meaning is:

$\left(x , y\right)$ is an ordered pair of numbers belonging to $\mathbb{R} \times \mathbb{R} = {\mathbb{R}}^{2}$. The first pair memeber belongs to the first set $\mathbb{R}$ and the second belongs to second $\mathbb{R}$. Althoug in this case is the same set $\mathbb{R}$. Could be in other cases $\mathbb{R} \times \mathbb{Z}$ or $\mathbb{Q} \times \mathbb{R}$

$\left(x , y\right)$ has the meaning of an aplication from $\mathbb{R}$ to $\mathbb{R}$ in which to every element x, the aplication asingns the y element.

$\left(x , y\right)$ has the meaning of plane's point coordinates. The first x is the horizontal coodinate (abscisa) and second is the vertical coordinate (ordenate). Both are coordinates.

$\left(x , y\right)$ has the meaning of a complex number: x is the real part and y is the imaginary part: $x + y i$

$\left(x , y\right)$ has the meaning of a plane's vector from origin of coordinates

etc...

You will see that meaning of $\left(x , y\right)$ could be whatever of above depending of context, but if you think a little bit, all meanings are quite similar

Hope this helps