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Singleton definition from Indicator function

  1. Mar 27, 2014 #1
    The attached image is from Wikipedia under the "Singleton" article.

    What reason is the first sentence beginning "Let S be a class..." necessary to the definition?

    I am confused by the words "defined by".

    I think I understand the second sentence:

    Take the second sentence beginning "Then S is called...":
    Assume S={p,q} where p≠q, then S is not a singleton because there exists some y ϵ S for some x ϵ S such that b(p) = (p≠q). For example if y=p:
    b(p) = (p=p)
    b(p) = (p≠q) <-breaks the singleton logic
     

    Attached Files:

  2. jcsd
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