So in Terence Tao's amazing book Analysis 1 he introduces the concept of ε close to aid in the understanding of Absolute Value. I have some trouble understanding the following on Proposition 2
(d) Let ε,δ > 0. If x and y are ε-close and z and w are δ-close, then x+z and y+w are (ε + δ)-close
and x-z and y-w are also (ε + δ) close