To prove that there exists a unique set such that for all is it as simple as choosing and so: ?
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I guess its right then? Thanks
Not quite. You have shown existence but not uniqueness.
To show uniqueness: We want to find a set such that . This means that and so that . By definition, (which is unique). And so it follows that and . Would this show uniqueness?
This what must be done.
Suppose that and . Then and . It follows that . Is this correct?
No that does not work. I think it is safe to say that most of us use this equivalence: . With that we can say if then that means . From which we can conclude that . QED
Why doesn't it work? ? Oh ok: Its apparent that if then . Sort of like a contradiction if we didn't have the empty set.
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