mth536_problem_7_2

mth536_problem_7_2 - MTH536 Chapter 7 Problem 2 Gene Quinn...

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Unformatted text preview: MTH536 Chapter 7 Problem 2 Gene Quinn – p. 1/ Chapter 7 Problem 2 By the ball centered at having radius ¥£ ¦¤¢ § ¨  ©      Prove that if   "! then ¡ we mean the set ¥ &¢ % ' ( ¥£ ¦&¢ §   # $  ¡  ¡ – p. 2/ Proof of Proposition Let be an arbitrary element of . Then   and by the proper ties of a metric    $ 0    $  $ !  ¥% ¢ '        $ !0 ) – p. 3/ Proof of Proposition Let be an arbitrary element of . Then   and by the proper ties of a metric    $ 0    $  $ !  ¥% ¢ '       By hypothesis, "!    $ !0  #  $ , so we may write  ¡ $ 0 ¡    $ $ !0  ¨ ¡  )        so by definition . Since was an arbitrary choice, ¥ ¦£ ¢ §  1 ¥ &¢ % ' ( ¥£ ¢ §  # – p. 3/ ...
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