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## Homework Statement

Find the interior of each set.

a.) {1/n : n[tex]\in[/tex]N}

b.) [0,3][tex]\cup[/tex](3,5)

c.) {r[tex]\in[/tex]Q:0<r<[tex]\sqrt{2}[/tex]}

d.) [0,2][tex]\cap[/tex][2,4]

I understand that b.)'s interior points are (0,5). I don't understand why the rest have int = empty set.

By definition, if there exist a neighborhood N of x such that N[tex]\subseteq[/tex]S, then x is an interior point of S. So for part d.), any points between 0 and 2 are, if I understand correctly, interior points. But the solution says that part d.)'s set of interior points is an empty set. Why is this?

Thank you

M