how do you create a vertical line with restrictions?

That would be a horizontal line melody 

I'd say  $$[(x,y)\in\mathbb{R^2}:x=c_1,c_2 \leq y \leq c_3]$$

Which stands for, x and y can both be any real number for which x is equal to c1 and y varies between c2 and c3

 It may seem a bit weird to say x is any real number for which it is equal to c1, but it's only an indicator for the type of values we are looking at (integers, complex numbers, postive values, etc.)

Reinout 

x=c    {c: r1 < c < r2 }

maybe?

where c is a given constant.

Umm no - but my c in the middle of r1 and r2 should have  been a y.  I still had x=c.

Just my notation was horrible inadequate and not correct.

I must get more familiar with number and set notation too!

My education is sorely lacking