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, and
$ 1 § 9 1 7© $ 1 9 ¦ 1 & § © 7 7 ¦" & @ © ¦ 7 & § © 7 " " ¡ ¢ ¦ © & & 87¤ 3 Suppose . Then by deﬁnition,
¤7 § 7 © ¤ 3 It follows that
¤£ ¨ © ¤7 § © & 7 © ¤7 @ ¡ ¢ and
¤ ¥£ ¡ ¦ § ¨ ¤£ Now suppose . Since is a sum of nonnegative terms, it can only be zero if each term is zero, in which case for all and by deﬁnition .
¡ ¢ ¦ § ¤ © § 7© § ¤7 $ ¨ ¦& – p. 5/ Proof that 4 and
§ © satisfy condition 2
, and
$ 1 § 9 1 7© $ 1 9 ¦ 1 & § © 7 7 ¦" & @ © ¦ 7 & § © 7 " " ¡ ¢ ¦ © & & 87¤ 3 Suppose . Then by deﬁnition,
¤7 § 7 © ¤ 3 It follows that
¤£ ¨ © ¤7 § © & 7 © ¤7 @ ¡ ¢ and
¤ ¥£ ¡ ¦ § ¨...
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This note was uploaded on 03/23/2010 for the course MATH 515 taught by Professor Staff during the Spring '08 term at Iowa State.
 Spring '08
 Staff
 Real Numbers

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