Consider the collection of open sets, (-n,n) from n=1 to infinity in R with the usual metric d(x,y) = abs(x-y). Use this collection of open sets to show R is not compact (make sure to prove R = UneJ(-n,n) as part of your work.

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A: Solve for limit

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Q: Prove that all points in the open interval (0,1) are limit-points (we are working on the real line)

A: Prove that all points in the open interval (0,1) are limit-points (we are working on the real line)

Q: dont understand what you have done in at the beggining

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Q: Prove

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Q: Make a diagram showing <PQR bisected by QX Choose a point Y on the ray opposite to QX.…

A: A ray is defined as a length whose one end is fixed but other end extends indefinitely.