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Let B = {((x,y) in R^2 | (x-10)^2 + (y-10)^2 <= 1}

then here "A intersection B" is the empty set.

Then let x_n be the sequence (0,10-(2/n)) which is a sequence in A and y_n be the sequence (10/n,10) which is a sequence in B.

would |x_n - y_n| tend to 0 in this case?