Is it possible to introduce infinitely large quantities without introducing infinitesimals?

Asked Apr 27 '20 at 23:27

Active Apr 27 '20 at 23:32

Viewed 46 times

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.

edited Apr 27 '20 at 23:32

asked Apr 27 '20 at 23:27

Anixx

10,161

Comments are not for extended discussion; this conversation has been moved to chat. – 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 $\infty$, and/or its fraction field $\Bbb R(x).,$ For background see literature on Hardy fields. 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

Is it possible to introduce infinitely large quantities without introducing infinitesimals?

0 Answers0