A. H. Lightstone

Albert Harold Lightstone (1926–1976) was a Canadian mathematician. He was one of the pioneers of non-standard analysis, a doctoral student of Abraham Robinson, and later a co-author with Robinson of the book Nonarchimedean Fields and Asymptotic Expansions.

Lightstone earned his PhD from the University of Toronto in 1955, under the supervision of Abraham Robinson; his thesis was entitled Contributions To The Theory Of Quantification. He was a professor of mathematics at Carleton University and Queen's University.

In his article "Infinitesimals" in the American Mathematical Monthly in 1972, Lightstone described an extended decimal notation for the hyperreals. Here there is a digit at every hypernatural rank rather than merely a digit for every rank given by a natural number. Such a hyperreal decimal is written as

Here the digit ${\displaystyle a_{H}}$ appears at rank ${\displaystyle H}$, which is a typical infinite hypernatural. The semicolon separates the digits at finite ranks from the digits at infinite ranks. Thus, the number 0.000...;...01, with digit "1" at infinite rank H, corresponds to the infinitesimal ${\displaystyle 10^{-H}}$.

...
Wikipedia