Example:

The key ingedient in the proof of this fact is the Cauchy-Schwartz Inequality. Apart from that, the proof is fairly straightforward.

The inequality in the second to last line is the Cauchy-Schwartz Inequality. The proof of the third property of metric spaces is now easily accomplished:

Analysis WebNotes by John Lindsay Orr.
Comments to the author: jorr@math.unl.edu

All contents copyright (C) 1996 John L. Orr
University of Nebraska--Lincoln
All rights reserved

Last modified: May 1996