Ordinals of countable order type beyond infinity
Channel: Nikolaj-K
Date: 2019-07-26

We implement an order of order type beyond the first infinite one, in a straight forward fashion. To that end, we arrange the natural numbers in an order with countably infinitely many jumps. So there are many numbers that come, with respect to our order, after an infinite amount of numbers. We might make a distinction between "bigger" and "comes after" to be explicit about not speaking about cardinal size of the sets involved.

https://en.wikipedia.org/wiki/Ordinal_number
https://en.wikipedia.org/wiki/Order_type
https://en.wikipedia.org/wiki/Epsilon_numbers_(mathematics)

I intent to soon move away from details about sets and move towards algebraic notions as used in dependently type programming language. Nonetheless, if you want to discuss these topics, maybe in a youtube stream, write me in the comments of just search for Nikolaj Kuntner on the web and pitch me a mail.