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2007-07-01 12:40:08 -07:00 · 2007-07-01 12:40:08 -07:00 · 74a1f5ec30
commit 74a1f5ec30
parent a3a5f79361
1 changed files with 9 additions and 0 deletions
--- a/ross-3.5.tex
+++ b/ross-3.5.tex
@ -10,3 +10,12 @@ By $-|b|\le b\le|b|$ we have
 $$-a\le-|b|\le b\le|b|\le a$$
 Hence $|b|\le a$ implies $-a\le b\le a$.

+\medskip
+Now prove the converse.
+By hypothesis we have
+$$b\le a\eqno(1)$$
+Also by hypothesis we have $-a\le b$ which implies
+$$-b\le a\eqno(2)$$
+Therefore by (1) and (2) we have
+$$|b|\le a$$
+