What is the name of this inequality?

[Leo Liu]

Homework Statement

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Relevant Equations

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My prof. calls it the triangle inequality. However the wikipedia page with the same this name shows a special case of it, which is $|x+y|\leq|x|+|y|$, and my prof. calls it the triangle inequality 2. I wonder what the formal name of the inequality in the picture above is. Thanks in adv.

 

[anuttarasammyak]

|(x-z)+(z-y)| \le |x-z|+|z-y|

 

[fresh_42]

Homework Statement:: .
Relevant Equations:: .

View attachment 288370
My prof. calls it the triangle inequality. However the wikipedia page with the same this name shows a special case of it, which is $|x+y|\leq|x|+|y|$, and my prof. calls it the triangle inequality 2. I wonder what the formal name of the inequality in the picture above is. Thanks in adv.

Triangle inequality is correct. The reason why is in post #2 by @anuttarasammyak .