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

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The discussion revolves around identifying the limit points, interior points, and boundary points of the set defined by {(x,y) | (x,y) = (1/n, 1-1/n)} for positive integers n. There is confusion regarding whether 0 and 1 are boundary points or limit points, with one participant asserting that they cannot be boundary points since they are not in the form of ordered pairs. The consensus is that all points, including limit and boundary points, must be expressed as ordered pairs in R2. The participants emphasize the need to clarify the definitions of limit and boundary points in this context. Understanding these concepts is crucial for accurately determining the nature of the set in question.
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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.

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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.
 
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"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!
 

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