- #1

goatsebear

- 13

- 0

## Homework Statement

Specify the boundary of the following sets. State whether the sets are open, closed, or neither.

1. {1 / n : n [tex]\in[/tex] N}2. { (x,y,z): x^2 + y^2 = z }3. { (x,y): 0 < x [tex]\leq[/tex] 4, 0 < y [tex]\leq[/tex] 4 }

**2. The attempt at a solution**

1. I want to say that the boundary is where n =/= 0 because then that would make the fraction an error. I think that the set is open because the equation does not include the boundary.2. I think that the boundary is the equation of x^2 + y^2 = z I'm not really sure on this one. Its more of a guess since I can't find any examples similar to it. Set would be closed since the equation includes the boundary.3. The boundary would be x = 0, x=4, y = 0, y =4. Would be neither since half of it includes the boundary and the other half does not.Thanks for any help.

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