Power Set of Natural Numbers is Countable


Authors : Sonia Sharma

Volume/Issue : Volume 7 - 2022, Issue 3 - March

Google Scholar : https://bit.ly/3IIfn9N

Scribd : https://bit.ly/3voCjGg

DOI : https://doi.org/10.5281/zenodo.6463282

This paper explains the Cardinality of the Power Set of Natural numbers. Set of Natural numbers is countable, in the same way the power set of Natural numbers is also countable as every subset of the Power set of Natural numbers is Countable. Prime numbers and Well ordering Principle play a very important role in proving this result. Since every Subset of Natural numbers is Countable, there exists a bijection between the Power Set of Natural numbers and a proper subset of Natural numbers.

Keywords : Subset, Power set , Order of a Power Set of a Set, Well ordering Principle, Prime Numbers, countable set, bijection, Uncountable Set.

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