|x - y|<=|x|+|y|

Does anyone know if the above is a true statment? Or is it just a lecture typo intending to be either:

|x + y|<=|x|+|y|

|x - y|<=|x|-|y|

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- Apr 3rd 2009, 09:46 AMpartyshoesTriangle Inequality
|x - y|<=|x|+|y|

Does anyone know if the above is a true statment? Or is it just a lecture typo intending to be either:

|x + y|<=|x|+|y|

|x - y|<=|x|-|y| - Apr 3rd 2009, 09:52 AMPlato
Is this true $\displaystyle |-y|=|y|~?$

Is this true $\displaystyle \left| {x - y} \right| = \left| {x + \left( { - y} \right)} \right| \leqslant \left| x \right| + \left| { - y} \right|~?$ - Apr 3rd 2009, 10:24 AMpartyshoesOhh , it is true!
Thanks (Sleepy)