Question

. The distance between two nonempty sets A ⊆ R and B ⊆ R is defined...

. The distance between two nonempty sets A ⊆ R and B ⊆ R is defined as follows: d(A,B) = inf{|a − b| | a ∈ A,b ∈ B}.

(a) Find the distance between A ={1/ n | n ∈ N } and B ={1 − 1 /n | n ∈ N }

(b) Give a proof or a counterexample for the following statement:

If d(A,B) > 0 then A ∩ B = ∅.

can someone please help me with this

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Feel free to ask any doubt in comment section. Thank you. ??

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