Is the above inequality true? I feel that it is, but I am having a tough time convincing myself (or coming up with an appropriate counter-example).
2026-02-23 16:58:33.1771865913
Is it true that $|x + y| \geq |x| - |y|$?
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$|x|=|x+y-y|\le|x+y|+|y|$ by the triangle inequality.