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# set watch

1. How do I prove a set is unique??Should I show it has some specific elements

2. Can you give us some context?
3. (Original post by generalebriety)

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.
4. If and and there are no other elements in C, then I'm not getting what you mean by 'unique', unless I'm missing something here.
5. (Original post by nuodai)
If and and there are no other elements in C, then 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. "
6. (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.
7. (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..
8. i really can't see what there is to prove. also having capitals for elements is retarded notation.
9. You can use the axiom of extensionality to prove that it's unique. (As wikipedia points out)
10. 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.)
11. it makes sense thanks ...

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