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Set mapping problem

  1. Mar 26, 2014 #1
    Let say i have two sets of numbers A and B. and I want to assigne to each number from A two slosest numbers from B. What i would do is to pick an elements from A and then go through the entire B set and find two closest. now if i go the other way arround in orderd to achieve the same result i would take an element from B and compare it to each element in A pick two closest and and assign that element from B to each of selected elements in A. this way i would gat a subset of B assigned to each A element for which i can the alpply the initaill approach. My question now is:

    "... i would take an element from B and compare it to each element in A pick two closest and and assign that element from B to each of selected elements in A." is two enough. Obviously not but what is ?? How do i calculate/prove that ??

    thnx

    b-boy

    PS

    this is my first post so please help me improve my question if it is not clear enough.
     
  2. jcsd
  3. Mar 26, 2014 #2

    Erland

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    Science Advisor

    Hmm... say you have A={1,2,3,4}, B={5,6,7,8}. Call your first assignment function F.

    Then F(1)=F(2)=F(3)=F(4)={5,6}.

    Now, call your second assignment function G. Then G(1)=G(2)=ø and G(3)=G(4)={5,6,7,8}, if I understand you correctly.

    So, this latter would not assign any values to 1 and 2, and all values are assigned to 3 and 4.

    To let G select more than 2 values would not solve the problem in a meaningful way either, as I understand it.
     
  4. Mar 26, 2014 #3
    yes you understood me correctly and pointed out something that i did not see. My cases were ususly two uniformly (more or less) distributed sets. A= {1,3,5,7} and B = {2,4,6,8} and A <<B. but now when you pointed the flaw in my logic i have to reconsider my problem , thank you.
     
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