MthT 430 Projects Chapter 1 Inequalities
MthT 430 Projects Chapter 1 Inequalities
This assignment should be typed.
The Triangle Inequality and Applications
For the time being, assume (P1) - (P12), and
|a| = ì
ï
í
ï
î
a,
a ³ 0
-a,
a £ 0.


The Triangle Inequality says that
|a + b| £ |a| + |b|.

On September 6, 2005, turn in well written solutions of Problems 1-3.


1.
Show that
|-b| = |b|.


2.
Show that
|a - b| £ |a| + |b|.
3.
Give examples such that
·
|a - b| = |a| + |b|.
·
|a - b| < |a| + |b|.



File translated from TEX by TTH, version 3.74.
On 07 Sep 2006, 13:17.