mth536_problem_7_1a

# 7 proof that let 2 5 3 4 7 7 7 2 7 2 7 2

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Unformatted text preview: ¤£ 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 . ¡ ¢ ¦ § ¤ © § ¨ ¦& By a similar argument, is the maximum of a set of nonnegative terms and can only be zero if each term is zero, which again implies that . ¡ ¤ © § © &  7© § ¤7 \$ – p. 5/ Proof that 4 and  satisfy condition 3 3 By the properties of absolute value, ¤7    ¤7 £ ¨ © 7 §  \$ 1 9 1  ¤7  ¦ § § 7 © 7  so interchanging 3 and leaves both and unchanged. ¤ § ¡ ¢ ¡ – p. 6/ Proof that Let ¤ ¦ ¦§ 2 5 3 4 ¡ ¦ § 7 © @  ¢ ¤ ¥£ ¨  6 . Then  ¤7  7 §  7 © @   ¤7  7 2 7 2 7 §  satisﬁes condition 4 – p. 7/ Proof that Let ¤...
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