Limit Points of Sets: Find Interior, Boundary & Open/Closed

[reddevils78]

Homework Statement

Consider the set in E^2 of points {(x,y)|(x,y)=(1/n,1-1/n), where n is a positive integar}. Find the limit points, interior points and boundary points. Determine whether this set is open or closed.

Homework Equations

The Attempt at a Solution

I figured, 0,1 must be the boundary points of the set but a mate claims they are the limit points instead that has brought me into this confusion of what exactly is the difference between the two.

 

[HallsofIvy]

"0" and "1" can't be boundary points of the set. This set is in R²- all points in it, all boundary points, all limit points, etc. must be of the form (a, b), an ordered pair of numbers, not a number. You and your mate both need to rethink the entire problem!