Recent content by hmb

Sorry, another mistake; in the first line it should say x \leq S, not x \in S.

OK, I think I've got part (d) now as well, although I think the 'hint' was supposed to read: [Hint: Let T' be the set of all partitions S with the property that every partition from T is a refinement of S . Show that supT = infT'.] I have attached the proof.

Sorry, the 5th-last line on the last page should read: For every x \in B and a \in A, \left[a\right]_{E_{x}} \subseteq \bigcap \left\{\left[a\right]_{E_{y}} \left| y \in T\right\}.

. . . and here is the last page.

OK, I think I have worked out part (c). I couldn't be bothered doing all the latex, so if you are interested I have attached my work as .JPG files.

Is the cell of a in infT the equivalence class of a modulo E_{infT}, i.e., [a]_{E_{infT}}? If so, then I think the properties the cell of a in infT would have would be as follows: For all a \in A, for all x \in T, [a]_{E_{infT}} \subseteq [a]_{E_{x}} and for all y \in Pt(A), if [a]_{E_{y}}...

This problem is from Hrbacek and Jech, Introduction to Set Theory, Third Edition, right at the end of chapter 2. Homework Statement Let A \neq {}; let Pt(A) be the set of all partitions of A. Define a relation \leq in Pt(A) by S_{1} \leq S_{2} if and only if for every C \in S_{1}...

Great, thank you for your help. I will take it that the corresponding definition of "least element" is correct as well then. Thanks again.

Homework Statement State the definitions of greatest and least elements in terms of strict orderings. Homework Equations Let \leq be an ordering of A and < be a strict ordering on A, and let B \subseteq A. b \in B is the greatest element of B in the ordering \leq if, for every x \in...

Homework Statement Prove: Let F and G be functions. F = G if and only if domF = domG and F(x) = G(x) for all x \in domF. Homework Equations ? The Attempt at a Solution If F = G, then (xFy if and only if xGy) (Substitutivity of identicals) If (xFy if and only if xGy), then...

Is it bad to replace a regulated AC adaptor that has an output rating of 9V DC and 200mA with a regulated AC adaptor of the same polarity that has an output rating of 9V DC and 1.7A? I know it's OK for the current rating to be higher than needed, but in this case the current rating on the new...

In parts of Brazil, the mains voltage is 127V AC. Is it safe to use an appliance which is supposed to take 117V AC in this situation? Thanks

Hello, How can I use an electronic device that takes 240V AC in an area where the power supply is 127V AC? Clearly I need a step-up transformer, but the only ones I can find convert 110/120V to 220/240V. If I use one of these, will it convert 127V AC to 254V AC (twice 127V)? If so, would it be...