This article discusses the uncountability of the power set of ℕ proven by using the out-indexes subset contradiction. Cantor’s theorem proves that the power set of ℕ is uncountable. This is a proof by contradiction. Suppose that the power set of ℕ is countable. This allows us to put all subsets of ℕ in a list. The contradiction will come from the indexes.

Please read the article at

PDF On the uncountability of the power set of ℕ

http://pengkuanonmaths.blogspot.com/2016/02/on-uncountability-of-power-set-of.html

or Word https://www.academia.edu/21601620/On_the_uncountability_of_the_power_set_of_N