## #math - Tue 20 Feb 2007 between 01:15 and 01:31

### NY Lost Funds

 medfly can anyone help me with my really really simple problem? :) thermoplyae Gotta passmedfly: Just write it TRWBW thermoplyae: maybe i'm not saying what i mean clearly. there is a bit in learning math that has to do with learning to push the envolope. after a short while, just re-solving variants on what you saw in class becomes unsatisfying thermoplyae Fair briareus sort of like watching the same cartoon over and over again everyday as you sit lonely in your prison celloops, wrong channel thermoplyae The one that took forever this past week was showing that there exist 2^d injections from an infinite set D to itself (with d = |D|) medfly ok, i got a parabola x^2-12x+36 and one of those 4 side shapes, where all the angles are equal to 90, starting at 0,0 and touching the parabola on a point. i need to find on what x would the circumference of the 4-side shape would it be smaller than 36 and bigger than 12.for some reason, everything i do doesnt come out right. TRWBW (i think he means perimeter) |Steve| mankind_tweezer: You were absolutely right about that condition. It is required for showing that the multiplication is well-defined. Thank you. TRWBW thermoplyae: is the trick to show D^2 has the same cardinality as D? thermoplyae Sure isn'tI don't thinkIf it is I'll certainly feel sillyWhere would you go with that? TRWBW thermoplyae: well if you did, then you could represent any relation on D (including a function of D->D) as characteristic function 2^D on a subset of DxD Dacicus I've been stumped on a problem for a while. I'm supposed to construct a bijection between sets of the form [a, b] and [a, b). I'm given the hint that there isn't an analytic formula (which hasn't been defined, btw). Any idea where to start? medfly anyone? :( thermoplyae medfly: Try letting the horizontal leg of the rectangle be of length 5.5 Dacicus medfly: What does "starting at 0,0" mean? Is that one of the vertices? medfly Dacicus, yeah, so double that point is the circumference.. Kasadkad Dacicus: Can you use the Schroder-Bernstein theorem? TRWBW thermoplyae: are you assuming axiom of choice? thermoplyae trwbw: I amThough we haven't talked about anything but Zorn's lemma yet medfly thermoplyae, why? thermoplyae medfly: Why not? If we pick a side length of 6, we get a perimeter of 12. Seemed like the logical thing to do Dacicus Kasadkad: We talked about it in class, but I can't see how to apply it. TRWBW well then injection 2^D into D->D injective seems simple, for f:D->{0,1} construct a g:D->D where for f(x)=0, g(x)=x, and for the rest just pick pairs to swap medfly thermoplyae, i thought we would get a perimeter of 12y, not 12, and i gotta get an answer like something>x>something..i just dont wanna say how i tried to solve it so i dont sound *too* stupid :( Kasadkad Dacicus: it shouldn't be hard to construct injections going in each direction thermoplyae TRWBW: I don't see itOh. mankind_tweezer |Steve|: glad it worked out thermoplyae I do see it, nevermind |Steve| And showing that each F_k is an ideal is trivial with that condition. mankind_tweezer right, that is the l=0 case