[originalcopying]

I had this idea but I did not know about this portrayal of it

that there are two ways to 'have' an infinity:

- by a lack of something. the classic original infinity. there is not a biggest number, they just keep going. it's a 'negative' definition; infinity because NOT finite.

- by construction. intuitionist or constructivist infinity (?). like a cycle or a going-back and forth never stopping. or with a self-referential _next-state_ arrow.

but I'm a bong smoking graduate student. as to the connection between all this and intutionism and/or constructivism? I really wish I knew or where in a position where I can discuss this with people; however I also think that internet randos like me need to await for whiter, wealthier, and more european academics from truly prestigious universities to decide what's what. Which does get in the way of getting myself into a position where I can understand this.

[qsort]

You're probably trying to say something but I don't understand what.

The way you 'have' infinity in math is by postulating there exists an inductive set (axiom of infinity in both ZF and NBG), and constructing other infinite sets using that as a building block.

Your first point is a definition of an infinite set (there are a bunch of equivalent ones), your second point is a statement of the axiom of infinity I assume?

[opnitro]

For natural numbers you can form that first one in terms of the second one. Natural number can be through of as an inductive construction.

Either:

- Zero

- 1+ (another natural number)