I think that the source is Richard Dedekind's Was sind und was sollen die Zahlen ? (Vieweg: Braunschweig, 1888).
I quote from the English translation : THE NATURE AND MEANING OF NUMBERS, (The Open Court Publishing Co., 1901) :
98. Definition [page 37]. If n is any number, then will we denote by Zn the system [set] of all numbers that are not greater than n [...].
106. Theorem [page 38]. If m < n, then is Zm proper part of Zn and conversely.