What's the other one?
Let's imagine there's a natural number exists between 7 and 8, and it is particularly sneaky so that it won't show up in any arithmetic operations performed by human and their devices. How we can argue it does not exist?
Let's imagine there's a natural number exists between 7 and 8, and it is particularly sneaky so that it won't show up in any arithmetic operations performed by human and their devices. How we can argue it does not exist?
8 is by definition the label for the number after 7. See https://en.wikipedia.org/wiki/Peano_axioms
So maybe you are thinking that there exists very different Set for natural numbers that has this nice properties, /
I think you can try an exercise to define such axioms and rules, see if actually they are consistent and not trivial and then see if they are different then the natural numbers.