# Tagged Questions

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### Axiom of Unions and its use of the existential quantifier

I'm reading Halmos's Naive Set Theory, and right now I'm on the section about the axiom of unions. As stated in the book, the axiom reads: For every collection of sets there exists a set that ...
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### Semantics and Logical structure in Definitons

Continuation of Free and bound variables in "if" statements definitions: A number is even if it is divisible by $2$. The number is even if it is divisible by $2$. Is the usage of the ...
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### Logical structure of definitions

Here are some "concepts" that are confusing me: The assertion $x>2$ is true when we replace $x$ by a number greater than $2$($3$ for example) and false if we replace it by $1$. But the assertion ...
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### Truth set of a Universal Quantifier and Family of sets

The definition of an intersection of family($F$) is: $$\cap F=\bigl\{x\mid\forall A(A\in F \implies x\in A)\bigr\}$$ If my understanding serves me correctly this notation means that all the $x$ ...
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### Definition of intersection of a family of sets

The definition of an intersection of family($F$) is: $$\cap F=\bigl\{x\mid\forall A: (A\in F \implies x\in A)\bigr\}$$ If my understanding serves me correctly this notation means that all the $x$ ...