How would I prove the triangle inequality for any three points a,b,c in the plane? The inequality needed to prove is $||a-b|| ≤ ||a-c|| + ||c-b||$
It throws me off when the subtractions are included. Please help.
2026-04-02 14:34:16.1775140456
How to prove triangle inequality?
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In the Euclidean norm, we have $\|a+b\|\leq \|a\| +\|b\|$.
Then $\|a-b\| = \| (a-c) + (c-b)\|$ and so by the above inequality, $\|a-b\| \leq \| a-c |+ \|c-b\|$.