Proof that $(a+b, a)$ belongs to $\mathbb{R}^2$ I am aware that the vector $(a+b, a)$ such that $a$, $b$ are real numbers belongs to $\mathbb{R}^2$, which is defined by any vectors $(x_1, x_2)$ such that $x_1, x_2$ are real numbers.
Is there a way to prove that $(a+b, b)$ indeed does equal $(x_1, x_2)$? The reason I am having trouble doing so it because the terms $a+b$ and $b$ have common variables (and hence are related), while $x_1$ and $x_2$ do not.
Any guidance would be appreciated. Thank you.

If $a,b \in \mathbb{R}$ then $a+b\in \mathbb{R} $ by closure of real numbers under addition. So, $(a+b, a)\in \mathbb{R}^2$.
