Blog post: pengkuan: On Cantor’s first proof of uncountability

Discussion about Cantor's first proof using the next-interval-function, potential and actual infinity. Cantor's first proof of the uncountability of real numbers is the first rigorous demonstration of the notion of uncountability. Countable sets can be put into a list indexed with natural numbers. If a set cannot be listed, then, it has more members than the set of natural numbers and is uncountable. Cantor's first proof is a proof by contradiction. First, he supposes that all real numbers are listed in any order by the list X=(x1, x2, x3 …). Then, a real number out of this list is found by using a series of intervals, contradicting that X lists all real numbers.

Please read the article at

PDF On Cantor's first proof of uncountability

http://pengkuanonmaths.blogspot.com/2016/02/on-cantors-first-proof-of-uncountability.html

or Word https://www.academia.edu/22104462/On_Cantors_first_proof_of_uncountability
Read and comment on the full post