The set of solutions for $y=x+1$ can be represented by a set of ordered pairs of the form $(y,x)$ or $(x,y)$ which is obviously always used. So these 2 sets define different subsets of $\mathbb R^2$, but i would graph them the same on the $x-y$ plane.
I'm confused because my notes say the element $(a,b)$ of $\mathbb R^2$ is represented by the point in the Cartesian plane whose $x$-coordinate is $a$ and $y$ coordinate is $b$, so where am I wrong?
thanks