anonymous
  • anonymous
what is the boundary of {1/n:n in N}
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
is it (0,1)??
anonymous
  • anonymous
Hmm, what is the definition of the boundary in this case?
anonymous
  • anonymous
well I thought boundary is just a point which has a neighborhood that contains points in the set and not in the set.

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anonymous
  • anonymous
I would think the boundary would be maybe \[ \{0\}\cup \{1\} \]
anonymous
  • anonymous
why would it be that and not include 1/2, 1/3, 1/4... etc.?
anonymous
  • anonymous
Oh, I see what you mean...
anonymous
  • anonymous
The boundary can't be in the interior, correct?
anonymous
  • anonymous
correct. this set does not have any interior points because every neighborhood of x must contain every point in the set.
anonymous
  • anonymous
Then the boundary is just the set itself.
anonymous
  • anonymous
so I would just say bd = {1/n}
anonymous
  • anonymous
\[ \partial \left\{\frac 1n:n \in N\right\} = \left\{\frac 1n:n \in N\right\} \]

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