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Mathematical notation

  1. Jul 20, 2005 #1
    T is an index set. And for each [tex]t \in T[/tex] [tex] A_t [/tex] is a set
    [tex]\bigcup_{t \in T} A_t = \{x : \exists t \in T with x \in A_t \}[/tex]
    What means this [tex]\bigcup[/tex] symbol and entire expression?
    And question on index set: is it used just for orderring any other set?
     
  2. jcsd
  3. Jul 20, 2005 #2

    Galileo

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    It's the union. If A and B are sets, [itex]A\cup B[/itex] denotes the union of A and B. It's that set which contains all the elements of A and those of B. So
    [tex]A \cup B = \{x|x\in A \vee x\in B\}[/tex]

    To generalize this to a union of an arbitrary number of sets is easy. That's exactly what your expression is: the union of all [itex]A_t[/itex].
     
  4. Jul 20, 2005 #3
    thank you very much, Galileo!
    What about my guess about "index set"?
     
  5. Jul 20, 2005 #4

    Galileo

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    I didn't understand what you meant exactly, but I think you have the right idea. The index set is just there to label the other sets. This way you can make T finite, countably infinite or uncountably infinite with the same notation. So the collection of sets A_t may be a finite, or infinite collection of any cardinality.
     
  6. Oct 25, 2009 #5
    I just stumbled onto this post and it relates exactly to what I'm trying to figure out. This concept of an index set is very baffling to me. Can you give a little more detail on what exactly an index set is?
     
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