Lines
It is not the case PQ is the line segement from the point P to the point Q. It is more like the line containing P and Q having magnitude Q – P. If PQ = ST, then PQS = 0 and so S = P + s(Q – P) for some s. Likewise, T = Q + t(Q – P) for some t. Hence ST = PQ + (t – s)PQ so s = t and Q – P = T – S.
This gives the first example of the boundary operator, ∂. It shows ∂PQ = Q – P is well defined.
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