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    How do I prove a set is unique??Should I show it has some specific elements
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    Wiki Support Team
    :confused:

    Can you give us some context?
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    (Original post by generalebriety)
    :confused:

    Can you give us some context?
    oops soory. iF A ∈ C , and B ∈C , and there are no other elements of C . The set is unique. How do I prove it?I have only started learning this , so pardon me if the answer is obvious.
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    If a \in C and b \in C and there are no other elements in C, then C = \{a, b\} I'm not getting what you mean by 'unique', unless I'm missing something here.
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    (Original post by nuodai)
    If a \in C and b \in C and there are no other elements in C, then C = \{a, b\} I'm not getting what you mean by 'unique', unless I'm missing something here.
    This is what my textbook says exactly:

    "For any A and B , there is a set C such that x∈C , if and only if x=A or x=B,So A ∈ C , and B ∈C , and there are no other elements of C . The set is unique. "
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    (Original post by rbnphlp)
    This is what my textbook says exactly:

    "For any A and B , there is a set C such that x∈C , if and only if x=A or x=B,So A ∈ C , and B ∈C , and there are no other elements of C . The set is unique. "
    Although it's still a bit unclear to me, why do you need to prove this? It looks like the book was giving a definition rather than something you have to prove.
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    (Original post by nuodai)
    Although it's still a bit unclear to me, why do you need to prove this? It looks like the book was giving a definition rather than something you have to prove.
    It then goes on to say prove it..:confused:
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    i really can't see what there is to prove. also having capitals for elements is retarded notation.
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    http://en.wikipedia.org/wiki/Axiom_of_pairing
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    You can use the axiom of extensionality to prove that it's unique. (As wikipedia points out)
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    Yeah, Simon is correct: this looks like a test of applying the axiom of extensionality (which says two sets are equal iff they have the same members.)
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    it makes sense thanks ...
 
 
 
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