Set up a Cartesian plane. On a sheet of paper mark two axes that cross at right angles - done. Excellent! We can work with that, just as long as you remember that paper and pencil aren't perfect. They have limitations.
You see, if you successively fold your sheet of paper in half, it becomes impossible after 6 or 7 foldings (even if you start with something as large a sheet of a newspaper or as thin as toilet tissue). Try it. Also, you can't draw a perfect line with a pencil as that line will always have a measurable width. That goes for pencil points too.
There cannot in reality exist a single point; it will always be a dot. And as such, they all have a measurable diameter. Geometrically, circles may only have six neighbors, no matter how small you make them. It's only at the infinite limit that a discontinuity arises and you suddenly find that a point may be in contact with an infinite number of surrounding neighbors.
