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## Homework Statement

Let set Q represent all rational numbers

[tex]\partial[/tex](Q[tex]^{int}[/tex]) = ?

[tex]\partial[/tex]((Q[tex]^{c}[/tex])[tex]^{int}[/tex]) = ?

[tex]\overline{(Q^{int})}[/tex] = ?

## Homework Equations

[tex]\partial[/tex]Q is the boundary of Q

Q^int is the set of interior points of Q

[tex]\overline{Q}[/tex] is the union of Q's boundary and Q

Q^c is Q's complement (in this case the set of irrational numbers)

## The Attempt at a Solution

I answered the empty set for all three. The interior of Q must be the empty set because any "ball" of values around Q will contain an unlimited number of both rational and irrational numbers. Thus there are no interior points. Now the boundary of the empty set would also be the empty set no?

Then the question is asked again but for the complement of Q. With the same reasoning, any ball around any irrational number in Q^c will contain rational numbers, so the set of internal points for Q^c is also the empty set. Boundary of which is again the empty set.

Finally the union of the boundary of Q^int and Q^int, must be the empty set because they both are empty.

So are my reasonings correct? I think they are, but it seems weird for my professor to ask these questions.