Re:Elementary Calculus: An Infinitesimal Approach (2000)
by hansvm on Thursday June 03, 2021 @02:17PM
(#27385261)
There are lots of different "infinities" floating around in mathematics, and that probably doesn't help the matter.
The extended reals or extended complex plane do behave as you describe (and infinite cardinalities have the same property), but infinitesimal treatments of calculus do not. You're instead working in an ordered field that contains the reals and some element greater than all reals.
Supposing such a thing can exist (they can exist in ZFC), the fact that you're working in an ordered field gives you a lot of infinitesimals and infinities (and also a lot of numbers "between" the ordinary reals).
The extended reals or extended complex plane do behave as you describe (and infinite cardinalities have the same property), but infinitesimal treatments of calculus do not. You're instead working in an ordered field that contains the reals and some element greater than all reals.
Supposing such a thing can exist (they can exist in ZFC), the fact that you're working in an ordered field gives you a lot of infinitesimals and infinities (and also a lot of numbers "between" the ordinary reals).