1

I want to extend the real numbers with infinitely large numbers. I envisage the resulting set being integral domain (there is division but by some elements we cannot divide).

Still, there are infinite quantities that are clearly invertible.

I wonder, is it possible to construct such set without infinitesimals?

If to add details, the inverses of some infinitely large elements are real numbers plus some non-real part.

Anixx
  • 8,488
  • 1
  • 26
  • 52
  • Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/107290/discussion-on-question-by-anixx-is-it-possible-to-introduce-infinitely-large-qua). – Asaf Karagila Apr 28 '20 at 06:44
  • @Anixx A simple example is the [ring $\Bbb R[x]$ of germs of real polynomial functions at $\infty$](https://math.stackexchange.com/a/49039/242), and/or its fraction field $\Bbb R(x).\,$ For background see literature on [Hardy fields](https://en.wikipedia.org/wiki/Hardy_field). See the comments moved to chat for much further discussion (including important context for the question which, alas, is now hidden in chat). – Bill Dubuque Apr 28 '20 at 20:17

0 Answers0