>>10833273>numberIdk, what are numbers? A number system can have infinite numbers, but no least infinite number, an example is , where the star map is not trivial.
If you take ordinals, or cardinals, as your number system, then and are the least infinite numbers. If you take , the least and only infinite number is .
The notion of "number" is generic and vague, but to say something is infinite we usually say that it's an upper bound of , or other equivalent notions. To find a copy of inside our number system, we would have to work in a category that has the natural numbers as the initial object. I'm not sure about the most natural framework. We would like our objects to be at least of the form , because we want to have a total order, we want to have , with homomorphism, be fixed (so that we can embed the natural numbers inside), and have at least one operation, not necessarily commutative. I'm not sure about what other costraints would be natural to impose
