Editing Infinitesimal (section)

=== Surreal numbers ===
Conway's [[surreal number]]s fall into category 2, except that the surreal numbers form a [[proper class]] and not a set.<ref name="Alling1985">{{citation | url = https://www.ams.org/journals/tran/1985-287-01/S0002-9947-1985-0766225-7/S0002-9947-1985-0766225-7.pdf | title = Conway's Field of surreal numbers | last = Alling | first = Norman | date = Jan 1985 | journal = Trans. Amer. Math. Soc. | volume = 287 | issue = 1 | pages = 365–386 | access-date = 2019-03-05 | doi=10.1090/s0002-9947-1985-0766225-7| doi-access = free }}</ref> They are a system designed to be as rich as possible in different sizes of numbers, but not necessarily for convenience in doing analysis, in the sense that every ordered field is a subfield of the surreal numbers.<ref name=bajnok>{{cite book|last=Bajnok|first=Béla|title=An Invitation to Abstract Mathematics|year=2013|publisher=Springer |isbn=9781461466369|quote=Theorem 24.29. The surreal number system is the largest ordered field|url=https://books.google.com/books?id=cNFzKnvxXoAC&q=%22surreal+numbers%22}}</ref> There is a natural extension of the exponential function to the surreal numbers.<ref name=G1986>{{cite book | last=Gonshor | first=Harry | title=An Introduction to the Theory of Surreal Numbers | year=1986 | publisher=Cambridge University Press | series=London Mathematical Society Lecture Note Series | volume=110 | isbn= 9780521312059 | doi=10.1017/CBO9780511629143 }}</ref>{{rp|at=ch. 10}}