How should we define set in ZFC?? I have heard sets are defined axiomatically in ZFC.But I have no idea why it is necessary to take zfc axioms to define set.It would be highly appreciated if anybody kindly explains it.Thanks in advance.
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1Actually I wanted to ask this question.But nobody did get me. – math is love Jan 11 '17 at 20:42
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Thr downvoters are requested to answer the question please. – math is love Jan 11 '17 at 20:48
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Actually, $\{1,1\}$ is a set. It's just that it's a set with one element, and it's equal to the set $\{1\}$. There is no such thing as a set with two equal elements (i.e. two elements who are equal to each other).
5xum
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@mathislove As you can see, the question already has an answer on another question: http://math.stackexchange.com/questions/742105/definition-of-set – 5xum Jan 13 '17 at 15:30
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It is not same..please read my question carefully..that is different. – math is love Jan 13 '17 at 15:33
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@mathislove Yeah but by now the question is so much different I have no idea what you are asking. I mean, how else would you define something other than by using axioms? – 5xum Jan 13 '17 at 15:34
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My question is why it felt necessary to define sets axiomatically .where did we get stuck in. – math is love Jan 13 '17 at 15:35
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@mathislove I understand. And my question is what other kind of definitions (not based on axioms) are there? – 5xum Jan 13 '17 at 15:36
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Tge downvoters re requested to pleqsr answer this question for this downvote I cannot even ask a question now. – math is love Jan 13 '17 at 15:36
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U did not get me..I don't know.probably there is none.but my qustion is the reason behind the formulation of Zfc – math is love Jan 13 '17 at 15:37