TITLE: Are the reals $\mathbb{R}$ a subset of $\mathbb{R}^2$?
QUESTION [5 upvotes]: Are the real numbers $\mathbb{R}$ a subset of $\mathbb{R}^2$?
$$\mathbb{R} \subset {\mathbb{R^2}}$$
Where $\mathbb{R}^2$ is defined as $\mathbb{R} \times \mathbb{R}$ whose elements are of the form $(x,y)$ where the notation $(.)$ denotes a pair and not an open interval and $x,y \in \mathbb{R}$.

REPLY [7 votes]: No the real numbers are not a subset of $\mathbb{R}^2$. 
In some contexts it may be useful to identify the real number $x$ with, for example, the couple $(x,0)$. (But you see there is no actual reason why $(x,0)$ rather than $(0,x)$ or maybe $(x,x)$.) Thus, this would need to be mentioned.