I’ve seen the full proof of the Triangle Inequality
However, I haven’t seen the proof of the reverse triangle inequality:
Would you please prove this using only the Triangle Inequality above?
Thank you very much.
Move |x| to the right hand side in the first inequality and |y| to the right hand side in the second inequality. We get
From absolute value properties, we know that |y−x|=|x−y|, and if t≥a and t≥−a then t≥|a|.
Combining these two facts together, we get the reverse triangle inequality: