medfly | can anyone help me with my really really simple problem? :) |

thermoplyae | Gotta pass medfly: 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 cell oops, 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't I don't think If it is I'll certainly feel silly Where 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 am Though 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 it Oh. |

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 |