definitions

The triangle inequality, or ordinary triangle inequality (OTI), is:

$$ |x+y| \le |x| + |y| $$

Examples:

• $x=2, y=3$
• $x = -2, y = 3$
• $x=2, y=-3$
• $x=-2, y=-3$

The reverse triangle inequality (RTI) is:

$$ |x-y| \ge ||x|-|y|| $$

Examples:

• $x=3, y=2$
• $x=2, y=3$
• $x=-2, y=3$
• $x=-3, y=-2$