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Martin
Frequent VisitorJoined: 19 Jan 2004Posts: 49
Location: Hong Kong
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Posted: Sat Aug 28, 2004 2:47 pm Post subject: Power set
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For any set S, prove that it is impossible to find a function from S onto the power set of S.
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Milton
Frequent VisitorJoined: 27 Oct 2003Posts: 182
Location: HKUST Math
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Posted: Sat Aug 28, 2004 9:30 pm Post subject:
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Let be such a map and be the index set such that . Define for , if and 0 otherwsie. Further define .
Let if and 1 otherwise, for . Let . Then for . As is onto, there is such that and for . However by the construction of , this is impossible since .
_________________Sometimes Truth is meanlingless;What means is how you believe in.
偶爾,真相並沒有意義;意義在於你怎樣相信。
Last edited by Milton on Sun Aug 29, 2004 2:00 pm; edited 1 time in total
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Martin
Frequent VisitorJoined: 19 Jan 2004Posts: 49
Location: Hong Kong
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Posted: Sun Aug 29, 2004 4:27 am Post subject:
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Thx, Milton.
But can you explain a little bit more about the last sentence? Why is that impossible?
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Milton
Frequent VisitorJoined: 27 Oct 2003Posts: 182
Location: HKUST Math
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Posted: Sun Aug 29, 2004 2:01 pm Post subject:
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To Martin, I have edited my original message to include more details. Please see if it is clear enough now._________________Sometimes Truth is meanlingless;What means is how you believe in.
偶爾,真相並沒有意義;意義在於你怎樣相信。
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Martin
Frequent VisitorJoined: 19 Jan 2004Posts: 49
Location: Hong Kong
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Posted: Tue Aug 31, 2004 2:51 am Post subject:
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Ya. I get it. Thanks for your clear explanation, Milton.
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