Question

why are integers called zahlen and denoted by z?

Answer 1

Q for the set of rational numbers and Z for the set of integers are apparently due to N. Bourbaki. (N. Bourbaki was a group of mostly French mathematicians which began meeting in the 1930s, aiming to write a thorough unified account of all mathematics.) The letters stand for the German Quotient and Zahlen. These notations occur in Bourbaki's Algébre, Chapter 1. Zahlen is a German word for number.

Answer 2

Why integer is called zahlen and denoted by Z:

• The notation Z came from the 1st letter of the German word Zahl, which means a number.  

• The German jargon for integer numbers explicitly is ganze Zahlen, which factually means whole numbers, and is the source for common, somewhat relatively casual usage by English-speaking mathematicians of whole number as a synonym for integer.

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