Posted: Sat Aug 28, 2004 2:47 pm    Post subject: Power set

For any set S, prove that it is impossible to find a function from S onto the power set of S.

Posted: Sat Aug 28, 2004 9:30 pm    Post subject:

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

Posted: Sun Aug 29, 2004 4:27 am    Post subject:

Thx, Milton.

But can you explain a little bit more about the last sentence? Why is that impossible?

Posted: Sun Aug 29, 2004 2:01 pm    Post subject:

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。

Posted: Tue Aug 31, 2004 2:51 am    Post subject:

Ya. I get it. Thanks for your clear explanation, Milton.