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
Abstract :
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.
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.
