>Let's imagine there's a natural number exists between 7 and 8 8 is by definition the label for the number after 7. See https://en.wikipedia.org/wiki/Peano_axi

>Let's imagine there's a natural number exists between 7 and 8 8 is by definition the label for the number after 7. See https://en.wikipedia.org/wiki/Peano_axioms 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.