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Reworded version:

I think I need to re-word as follow:

Can a nonempty set X with P(X)=0?

Suppose F to be a non-empty set with [tex]P(F)\neq 0[/tex]. Call its closure be F'.

Now let set theoretic different F'\F be A. Clearly, A could be non-empty.

Is this the case where P(A)=0?

Is not, how do you relate P(F) and P(F')?

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Original version:

Can a nonempty set X has P(X)=0?

My thought is suppose a nonempty set F then its closure F'\F=A where P(A)=0.

Is this true??

I think I need to re-word as follow:

Can a nonempty set X with P(X)=0?

Suppose F to be a non-empty set with [tex]P(F)\neq 0[/tex]. Call its closure be F'.

Now let set theoretic different F'\F be A. Clearly, A could be non-empty.

Is this the case where P(A)=0?

Is not, how do you relate P(F) and P(F')?

=================================

Original version:

Can a nonempty set X has P(X)=0?

My thought is suppose a nonempty set F then its closure F'\F=A where P(A)=0.

Is this true??

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