mth536_problem_7_1a

# 6 5 p 4 proof that 4 and satisfy

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Unformatted text preview: condition 1 ¨ ¤ §   ¤ §      § ©  3 ¢ ¤£ ¡ 3 is a sum of nonnegative reals for all ¤£  ¨ ¤ ! ¦ ,   is always  # .  6 ¢ ¤ § 5  ¦ ¤ ¡ §   § ¡ ©   ¦ ¦" " " is the maximum of a ﬁnite set of nonnegative real numbers, so for all , is always .  6  § 5 ¦ ¡ % & ¤ ¦   § % & – p. 4/ Proof that 4 and § ©  satisfy condition 2 , and \$ 1 § 9 1 7© \$ 1 9 ¦ 1 87¤ 3 Suppose . Then by deﬁnition, ¤7   § 7 © ¤ 3 ¦& – p. 5/ Proof that and ¤ © § ¡ ¤ ¥£ ¦ § ¨ ¦ § ¨ 7  ¤7  @  7 §  ©   ¦" & " " ¦ & © & © & 1 @  & 7 ©  1 9 1 \$ ©  ¤7  © 7 §  1 9 7 §  ¦& \$ ¦  © 7 ¡ ¢  ¤£ ¤7  Suppose It follows that . Then by deﬁnition, 87¤ 7© § 3 4 and 3  satisfy condition 2 , and – p. 5/ Proof that 4 and § ©  satisfy c...
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