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Prove the triangle inequality.

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Lesson Parent:

Problem:

Prove the triangle inequality. The triangle inequality says that $|A+B|\leq |A|+|B|$ where $A$ and $B$ are real numbers.

Answer:

It is true that $|A+B|\leq |A|+|B|$ where $A$ and $B$ are real numbers.

Solution:

Note that

where the second line comes from the fact that <Sign in to see all the formulas>.

Because the absolute value can be defined as <Sign in to see all the formulas> then