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

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medflycan anyone help me with my really really simple problem? :)
thermoplyaeGotta pass
medfly: Just write it
TRWBWthermoplyae: 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
thermoplyaeFair
briareussort of like watching the same cartoon over and over again everyday as you sit lonely in your prison cell
oops, wrong channel
thermoplyaeThe 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|)
medflyok, 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.
TRWBWthermoplyae: is the trick to show D^2 has the same cardinality as D?
thermoplyaeSure isn't
I don't think
If it is I'll certainly feel silly
Where would you go with that?
TRWBWthermoplyae: 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
DacicusI'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?
medflyanyone? :(
thermoplyaemedfly: Try letting the horizontal leg of the rectangle be of length 5.5
Dacicusmedfly: What does "starting at 0,0" mean? Is that one of the vertices?
medflyDacicus, yeah, so double that point is the circumference..
KasadkadDacicus: Can you use the Schroder-Bernstein theorem?
TRWBWthermoplyae: are you assuming axiom of choice?
thermoplyaetrwbw: I am
Though we haven't talked about anything but Zorn's lemma yet
medflythermoplyae, why?
thermoplyaemedfly: Why not? If we pick a side length of 6, we get a perimeter of 12. Seemed like the logical thing to do
DacicusKasadkad: We talked about it in class, but I can't see how to apply it.
TRWBWwell 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
medflythermoplyae, 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 :(
KasadkadDacicus: it shouldn't be hard to construct injections going in each direction
thermoplyaeTRWBW: I don't see it
Oh.
mankind_tweezer|Steve|: glad it worked out
thermoplyaeI do see it, nevermind
|Steve|And showing that each F_k is an ideal is trivial with that condition.
mankind_tweezerright, that is the l=0 case

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