TITLE: Who first defined quantum integers?
QUESTION [9 upvotes]: Who first gave the definition of quantum integers
$$  [m]_q = \frac{1 - q^m}{1 - q} $$ and addition as
$$ [m]_q \oplus_q [n]_q = [m]_q + q^m [n]_q $$ and multiplication as 
$$ [m]_q \otimes_q [n]_q = [m]_q [n]_{q^m} $$
and in which context?

REPLY [5 votes]: I think q-integers were first introduced by F.H. Jackson in 1903 in the paper http://www.biodiversitylibrary.org/item/130137#page/15/mode/1up (On generalized functions of Legendre and Bessel).