I've been trained in applied mathematics, and I just started exploring pure mathematics (real analysis, to be exact). I'm already stuck at a very simple proof, and was wondering if anybody can help me out: http://img392.imageshack.us/img392/8971/proofeg2.png I understand it for the most part. However, I do not understand why the statement highlighted in yellow implies the statement that is highlighted in red. I copied that proof directly from Maxwell Rossenlicht's Introduction to Analysis. Any help is greatly appreciated.