Creation of binary lists, discussion about the power set of ℕ, the diagonal argument, Cantor’s first proof and uncountability. Binary system is kind of magic because it can express natural numbers, real numbers and subsets of natural numbers. Below, we will create lists of binary sequences to study the uncountability of the power set of ℕ and real numbers.

1.Infinite list of binary sequences

2.About the Power set of ℕ

3.Frame of Natural Infinity

4.List of numbers smaller than 1

a.Creation of the numbers

b.Denseness of R..

c.Completeness of R..

d.Real numbers in [0,1[

5.About Cantor’s first proof

6.About the diagonal argument

7.Conclusion

Please read the article at

PDF Lists of binary sequences and uncountability

http://pengkuanonmaths.blogspot.com/2016/11/lists-of-binary-sequences-and.html

or Word https://www.academia.edu/30072323/Lists_of_binary_sequences_and_uncountability