The $y$-axis can be written as a set like this $\{x=0:y\in\mathbb{R}\}$, right?

@johnny09 Did you want to write $\{(x,y); x=0, y\in\mathbb R\}$?

@MartinSleziak Yes, I must define that the set contains pair of coordinates. So, I need $(x,y)$ where $x=0$ and $y$ a real number. Thank you.

I mean the set which contains elements with $y=kx^n$.

@johnny09 Yes. You're missing $\in$ there. I guess it is just a typo.

And I don't think you need $y$, since it does not appear there at all.

Yes, I forgot the symbol and can't edit it.

You can simply write $\{(x,kx^n); x\in \mathbb R\}$.

You do no have to write $x,y\in \mathbb R$ if there is no $y$.

Of course, you can write the same set as $\{(x,y); y=kx^n; x,y\in\mathbb R\}$.

Alright. Thanks.