An infinitesimal monad of a hyperreal number 
is the set of
hyperreal numbers 
for which 
is smaller than every positive real
number. Writing 
for the hyperreal numbers, it is
 |
where 
ranges over the ordinary positive integers (Keisler
2007, p. 2). The center 
belongs to 
. In particular, 
consists of all infinitesimals,
including 0 under the convention used in nonstandard
analysis. Two infinitesimal monads are either equal
or disjoint (Keisler 2007, p. 4).
This meaning of monad is distinct from the monad of category theory.
