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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Naive set theory
Replies: 4   Last Post: Apr 9, 2013 3:02 PM

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Aatu Koskensilta

Posts: 2,612
Registered: 6/28/08
Re: Naive set theory
Posted: Apr 9, 2013 10:03 AM
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Zuhair <zaljohar@gmail.com> writes:

> What's the proof of the following in naive set theory?
>
> Not exist x. x is empty

By Russell's paradox, there exists a set R such that R in R and R not
in R. By ex falso quodlibet, there is no set with no elements.

--
Aatu Koskensilta (aatu.koskensilta@uta.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus

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