[zelphirkalt]

In German though "Ganze Zahlen" is not ambiguous. At least in my entire life I have not seen any other understanding of it and every child at school learns about them and that they include 0 and negative numbers, in contrast to natural numbers ("Natürliche Zahlen").

[freilanzer]

As a German, this is exactly what whole numbers means - numbers such as -1, 0, 1. Natural numbers are whole numbers > 0.

[ahf8Aithaex7Nai]

Every mathematical introductory text that excludes zero from the natural numbers contains an unwieldy additional notation like N_0 in the very next sentence. Why the hell should the number that is both used in the first Peano axiom and is the additive neutral element of the natural numbers not be included in the natural numbers? I've never understood why so many people insist on this, relying on pseudo-anthropological reasoning or something. Zero is at least two and a half thousand years old. You could just as easily claim that the natural numbers end with the number 10 because humans don't have any more fingers.

[jacobolus]

Okay, but what about in the 1880s?

[weinzierl]

I think, historically the term "Ganze Zahl" (a whole or entire = integer number) was always used in contrast to "Gebrochene Zahl", meaning broken or fractured number.

Negative numbers are not broken, so they have always been considered whole. For example, Leonhard Euler wrote in his "Vollständige Anleitung zur Algebra" from 1767:

"Alle diese Zahlen, so wohl positive als negative, führen den bekannten Nahmen der gantzen Zahlen, welche also entweder größer oder kleiner sind als nichts. Man nennt dieselbe gantze Zahlen um sie von den gebrochenen, und noch vielerley andern Zahlen, wovon unten gehandelt werden wird, zu unterscheiden."

https://www.math.uni-bielefeld.de/~sieben/Euler_Algebra.ocr....