Questions tagged [set-theory]

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7answers
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Selection of logical connectives {¬,∨,∧,⇒,⇔} in set theory?

Nearly every treatment of set theory, whether Paul Halmos' Naive Set Theory, Herbert Enderton's Elements of Set Theory, Patrick Suppes' Axiomatic Set Theory, etc. introduce a common set of logical ...
2
votes
2answers
160 views

Prove a logical formula is equivalent to the contradiction if and only if the set it describes is empty

Let ψ be a well-formed-formula (wff). Prove that (ψ ≡ ⊥) ⇔ {x:ψ(x)}=Ø that is, the formula ψ is a contradiction if and only if the set it describes has no members. Note This question is not about ...
6
votes
5answers
2k views

How many empty sets are there?

Thre are many sets with a single object, for example the set which only contains the statue of liberty or the set which contains my copy of Catch-22. But how many sets are there that contain nothing? ...
7
votes
11answers
2k views

Proof Universe Came From Nothing?

Consider the following proof: (1) Let the Universe be defined as the set of all things. (2) It is impossible for a thing to come from itself. (You can't be your own parent) (3) 2 implies a set of ...

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