> in English whole numbers mean 0, 1, 2, ...
According to Wikipedia [1], the term is ambiguous. Its talk page [2] has plenty discussion about it though.
According to Wikipedia [1], the term is ambiguous. Its talk page [2] has plenty discussion about it though.
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....
I’m not sure about that ”and never was”. Mathematicians used to have fairly loose definitions for all kinds of things and different fields sometimes have incompatible definitions for a term, so I think it’s not impossible “ganzzahlig” was used ambiguously for ℤ or ℕ (in- or excluding zero) for a while in some corners.
When was the phrase “natural number” even invented? The best I can find is https://jeff560.tripod.com/n.html (via https://mathoverflow.net/questions/379699/origin-of-phrase-n...) which says “Chuquet (1484) used the term progression naturelle for the sequence 1, 2, 3, 4, etc.”
There may well have been a time where “ganzzahlig” existed but “Natürliche Zahl” didn’t yet.
Inteiros - (...-2, -1, 0, 1, 2...)
Naturais - (1, 2, 3...)
No, it is not even a real number, but every whole number surely is a real number.
Yes, it is a "Gaußsche ganze Zahl".