3 ms·

Because subtraction is not a total operation on positive integers. Negative numbers leave the domain.

• CamperBob2 2mo ago
  Why was it important to Tarski to limit the domain to positive integers? That seems pointlessly arbitrary.
  • LPisGood 2mo ago
    Truly, you could say that about many conjectures, especially more “fun” classical ones.
  • QuesnayJr 2mo ago
    If you allow negative integers, you get negative exponents. To accomodate negative exponents, you can expand the domain again, to rational numbers. If you allow rational numbers, then you have to allow rational exponents, which means you can take arbitrary nth roots. Which you could do, but now you're most of the way to the complex numbers (plus roots aren't unique anymore).