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Sets and notation

  1. Nov 8, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    If I have a set R and a function T, then what does the following mean: T: R x R -> R?

    Also, when I have a set A and a set B, then does the following mean that all elements in A are equal to all elements in B? A [itex]\subseteq[/itex] B
     
  2. jcsd
  3. Nov 8, 2009 #2

    HallsofIvy

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    RxR, the Cartesian product, is the set of all pairs, (x,y), where each of x and y is in R. T: R x R->R means that T is a function that, to every such pair, (x,y), assigns a member of R.

    Operations are often represented that way. For example, if R is the set of real numbers, R x R is the set of pairs of real numbers and addition, "+", assigns a single number to every pair of numbers: T(x,y)= x+ y so T: R x R-> R.

    No, not if by "all elements in A are equal to all elements in B" you mean they are the same set. [itex]A \subset A[/itex] means that all elements of A are in B, but there are some elements of B that are not in A. [itex]A\subseteq B[/itex] includes the possibility that there are no elements of B that are not in A- the possiblility that A= B.
     
  4. Nov 8, 2009 #3
    Thank you. Two very good answers for two questions.

    That cleared things up.
     
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