Such notations are indeed of interest in the theory of surreal numbers; they are called gaps. Let the class of surreal numbers S=L∪R, and for every l∈L,r∈R: ll]}; R={r: r is a positive infinite number}.
 L={l: l is a negative, or zero, or a positive infinitesimal number [i.e. for every positive real number x: x>l]}; R={r: r is a non-infinitesimal positive number }.
(Of course, such notations are not surreal numbers.) -