This worksheet illustrates Theorem 2.8 (The Triangle Inequality) from the lecture notes.

[list=1] [*] Move [color=#0000ff][math]a[/math][/color] and [color=#0000ff][math]b[/math][/color], and see what happens to [color=#006400][math]|a|[/math][/color], [color=#006400][math]|b|[/math][/color], [color=#ff0000][math]|a|{+}|b|[/math][/color] and [color=#660099][math]|a{+}b|[/math][/color]. [*] When does [color=#0000ff][math]a[/math][/color][math]=[/math][color=#006400][math]|a|[/math][/color]? [*] When does [color=#ff0000][math]|a|{+}|b|[/math][/color] [math]=[/math] [color=#660099][math]|a{+}b|[/math][/color]? [/list]