## #math - Wed 7 Mar 2007 between 00:00 and 00:47

### NY Lost Funds

 TRWBW noway-: is this the same problem as yesterday? noway- Yes :-/http://www.mathbin.net/8735Should I use the fact that every element of A is also a subset of A. Then since P(A) is all the subsets of A, every element in P(A) will a set with elements from A. Then relate the two?will be a* TRWBW noway-: s in P(A) implies s sub A. that's just the definition of P(A). x in S sub A => x in A => x sub A from the hypothesis. x sub A => x in P(A), again by definition of P(A). so x in S => x in P(A), which implies S sub P(A)noway-: i think the key thing here is to see: S in P(A) <=> S sub A. they are completely the same thing. noway- okis see it more clear now, thank you TRWBW np noway- the second part, x in S sub A => x in A => x sub A, was kinda catching me up a bit raz0 number E-12 is number * 10^(-12), isn't it? LoganCapaldo usu. raz0 got it koro kercyr, i'm here prettytoney Hi.Did that guy prove his set theory thing? kercyr There is a countable abelian group where every element has order 2. koro yeah i saw the backlog prettytoney He was on earlier, I forget the question exactly. S \in P(A) => S \subset P(A), where P is a power set. koro so it's not true that every abelian group of order 2 is isomorphic to Z_2^n for some n? kercyr right. koro er, with every element of order 2 i mean TRWBW PRETTYTONEY: he had been working on it for 2 days so i gave him the answer. i ran out of hints. prettytoney haha, ok. kercyr But it's true that the group is isomorphic to a direct sum of Z_2's. Knight_Lord Can I numerically compute df/dx^2 without computing df/dx? koro oh? Knight_Lord From a 2D function koro i thought Z_2^n was the same as Z_2 + ... + Z_2 (n times)whatever that means when n is infinite TRWBW koro: think of operating over P(R) with A+B=C given by C=(AuB)-(AnB) kercyr Z_2^n is the set of functions from {0,1,..., n-1} to Z_2. Knight_Lord How to compute df/dxy numerically? koro kercyr: oh so direct sum means with all but finitely many coordinates being nonzero? kercyr right. prettytoney How did it go, trwbw? Got a hint for me? kercyr uh... TRWBW kercyr: given any set S, that operation i gave over the powerset of S is isomporphic to Z_2^S koro oh well i told you my algebra was shitty