Metric Spaces
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A metric space is defined to be a pair (M,d)
where M is a set (whose members are called points) and d is a real
valued function on pairs of points of M, such that the following
conditions hold:
- Symmetry.
If p,q are points, then d(p,q) = d(q,p).
We write pq for d(p,q), so the symmetry condition can be written as:
pq = qp
- Triangle Inequality.
For any three points p,q,r in M:
pr <= pq + qr
- If pq = 0, then p = q.