Although I like the idea of this post I think you can explain it simpler since you are only considering countable infinity. Of course if you add a single element to something which is countable it will still remain countable.
You are viewing a single comment's thread from:
Since the post is aimed at the layman and tries to lay the foundations of the mathematical idea of infinity I felt a thorough explanation/proof was needed. Also I would argue that it is not so obvious. When I first learned about this it took a bit of getting used to.
And psssst... your spoiling things. Just kidding. The next part of this series will be about uncountable sets and diagonalization. After all I haven't even introduced the name "countable infinity" yet, because so far we have only looked at one type of infinity.
I guess it is a matter of taste. But I do think that countability is a natural concept since it essentially corresponds to counting. Countability in a finite setting then gives rise to countability in an infinite setting.
@blackiris wrote a nice post about the basic concept of infinity. If you have free time check it out :) https://steemit.com/mathematics/@blackiris/lamentations-in-a-sanatorium
Well, the title of the post sure does sound promising! :D I will make sure to give it a read.
Thanks for your input! :)