Two Points with Infinite Distance I have tried looking for an answer to this, but can't seem to find anything. 
Is it possible on a standard Cartesian grid to define two (or more) points with infinite or undefined distance from each other? 
If yes, please provide an example. If no, please explain. Thanks!
 A: No.
Being on the standard Cartesian grid would mean the points in hand have real (or, integer) coordinates. However, the distance of points $(a_1,a_2,\dots,a_n)$ and $(b_1,b_2,\dots,b_n)$ in $n$ dimension can be calculated by $\sqrt{(a_1-b_1)^2+\dots+(a_n-b_n)^2}$, which is a finite real number for any given real coordinates.

Yes.
We power mathematics, and we can define whatever we like, e.g., given the standard Cartesian grid, we can introduce (even define with proper terms) an 'endpoint' at infinity for every line - if we wish, even two for both directions. Then (if we still insist on 'distance' and its nice properties), their distance to ordinary points will be necessarily infinite.
A: Let's assume we have two such points, $A$ and $B$. Then there would be a line $\vec{AB}$ connecting the two points. If this line is not already the $x$ axis, allow us to rotate the Cartesian plane such that it is.
If $A=(x,0)$ what could $B$ possibly equal? We would need to have:
$$|B-A|=(\infty,0)$$
Therefore there could not be any representation of $B$ as a point in the Cartesian plane, since every point has a finite $x$ and $y$ coordinate, and the difference of no two finite numbers is infinite. 
Hence we cannot have two points with infinite distance without adding points which we define to be "infinitely distant" to the plane; i.e. it is impossible for the standard Cartesian plane.
This Wikipedia article will probably be of interest to you: https://en.wikipedia.org/wiki/Point_at_infinity
A: Tag of "soft question" would match. A kind of paradox, as a plane (or line) as representative of complex or real are unbounded but for two given elements there is always a certain distance, however rhe distance is unlimited.
