A line extends in both directions infinitely, marks the shortest distance between two points, and can be straight or curved. It is purely mental - there are precious few lines in real life - and cannot be crossed. Or can it?
y=1 completely divides the cartesian plane in two. You are on one side or the other, because by definition a line has no width, only length. It is completely one dimensional.
But what about...
y=x/x=1? This line has a hole...and can be crossed. Is this what exists in my mind? Nah. It's more like...
y=(x^2-1)/(x^2-1)=1 or
y=(x^3-2x^2-x-1)/(x^3-2x^2-x-1)=1. Positively Holey! :-p
Don't ask me if it's true. I'll deny it. :)
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