Easy Way to See Reverse Triangle Inequality

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:

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 .

Related Posts

Handy command line benchmarking tool

Stan Rogers

Ultimate Hot Couch Guy

Quote on Java Generics

The Programmer Tendency

Figure out undocumented JSON with gron

Mental Model of Dental Hygiene

Book Review: Swastika Night

Is there a name for this construction?

Fun with negation and idioms