Which of the following sets are totally bounded? Give reasons for your answer. Are they compact?
i) 2N in (N,d) where d is the discrete metric.
ii)  in (R,d) where d is the Euclidean metric. 

Let's analyze each set:

i) \(2\mathbb{N}\) in \((\mathbb{N}, d)\) where \(d\) is the discrete metric:
- The discrete metric \(d\) between any two distinct points is always 1 if the points are distinct, and 0 if they are the same.
- \(2\mathbb{N}\) consists of all even natural numbers.
- Since each point in \(2\mathbb{N}\) is isolated (the distance between any two distinct points is 1), any __________ _____ ________ ______ ____ _______ _____.
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