On this wikipedia page for the triangle inequality, it states the triangle inequality for norms:
$||x+y|| \leq ||x|| + ||y||$
but on this example about the French Railway Metric I found (page 19), it uses an equality instead. Why is this the case?
2026-04-23 05:51:19.1776923479
When does the triangle inequality apply for norms?
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The example given in those notes on page 19-20 does not use the triangle inequality at all, except for saying that the user can verify that the metric function satisfies the properties needed for a distance function (one of which is the triangle inequality). So it does not "use an equallity instead."