## To Show

## Easy Way To See It

Remember that the absolute value/norm of the difference of 2 vectors is the distance between them. Rewrite as and as .

Now we want to show $$d( | x | , | y | ) \leq d(x, y)$$. |

But this is obvious. Making both terms the same sign can only put them
on the same side of the number line, which can never *increase* the
distance between them.

And this is why I prefer to .