Answer to Question #310456 in Real Analysis for Nikhil Singh

Question

Check the whether the set { 2/7, 2/8, 2/9,..} is countable or not. Also a give example of proper subset of R which is uncountable

Answer 1

The set is countable since there is a bijection between the wet and $\mathbb{N}$ : $f(2/n)=n-7$ .

$(0,1)$ is a proper unbounded set which is uncountable (it is continuum)