The title is a bit absurd, we could examine the distance of any number from itself..

In the previous post I examined the property of distance being even or uneven. Let’s go back to distance of zero from itself. Formally the distance of zero from itself is |0 – 0| = 0. 0 mod 2 = 0, why isn’t this distance even?

The distance doesn’t exist, instead of distance we have a point. Euclid’s definition to a point is: “A point is that which has no part.” In Euclid words the “distance” of zero from itself, |0 – 0| = 0 has no part. Something like this isn’t even or uneven.

In an e-book called “The Way To Geometry” it says, that magnitude of a point is zero.

Philosophically speaking a point is what Democritus called “atomos” applied to geometry.

In short, there isn’t distance of zero from itself. The meaning of distance |0 – 0| = 0 is geometrically a point, something that has no part.