Axiom:Identity of Equidistance

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Axiom

Let $\equiv$ be the relation of equidistance.

Let $=$ be the relation of equality.


Then the following axiom is imposed:

$\forall a, b, c: ab \equiv cc \implies a = b$

where $a, b, c$ are points.


Intuition

If two points have no distance between them, they are the same point.


Also see


Sources