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.
How should we define set on ZFC?
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elementary-set-theory
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1Actually I wanted to ask this question.But nobody did get me. – 2017-01-11
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0Thr downvoters are requested to answer the question please. – 2017-01-11
1 Answers
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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).
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0Will anybody please naswer my question without downvoting it? – 2017-01-13
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0@mathislove As you can see, the question already has an answer on another question: http://math.stackexchange.com/questions/742105/definition-of-set – 2017-01-13
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0It is not same..please read my question carefully..that is different. – 2017-01-13
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0@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? – 2017-01-13
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0My question is why it felt necessary to define sets axiomatically .where did we get stuck in. – 2017-01-13
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0@mathislove I understand. And my question is what other kind of definitions (not based on axioms) are there? – 2017-01-13
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0Tge downvoters re requested to pleqsr answer this question for this downvote I cannot even ask a question now. – 2017-01-13
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0U did not get me..I don't know.probably there is none.but my qustion is the reason behind the formulation of Zfc – 2017-01-13