Definition talk:Natural Numbers/Historical Note

From ProofWiki
Jump to navigation Jump to search

Hmm, interesting. I always thought it went: 'God created the integers'. I even have a book by Hawking on my shelf titled by that very quote. An opportunity to put an erratum on one page or another? --Ascii 18:17, 1 October 2019 (EDT)

Interesting. This has inspired some research.
The word actually used was Zahlen, which in German (according to Wiktionary -- please bear with me, German is not my first language) means (in this context) number (any number, often in the context of the amount you are supposed to pay in the restaurant, it seems) or numeral. It is frequently translated integer in various contexts, notably the use of $\Z$ for the set of integers, because in many contexts (including a lot of number-theoretical ones) the distinction may not be important. But ganze Zahl (literally whole number) is "actually" German for integer -- again, so says Wiktionary.
As Kronecker was using it here, it can be argued that "natural numbers" was indeed what he meant. Remember the controversy up until even the 17th century as to whether or not $0$ is a number, let alone the existential angst brought about in medieval times when the idea of negative numbers was raised. So to that end, negative numbers are also a man-made creation.
Rather than an erratum page, it may be worth expanding this one to explain the differences and subtleties. But it will need someone who knows precisely what they are doing (rather than googlesearching), or who can lay their hands on a suitably authoritative source work. --prime mover (talk) 01:33, 2 October 2019 (EDT)
addendum: I have that Hawking book myself on my shelf, but it's right in the bottom corner and I'll have to move a stack of CDs to reach it so as to be able to check whether he actually discusses that quote in detail. Haven't read it for a few years, I got it soon after it came out, along with Penrose's "The Road to Reality", and read them both over the course of a few months on the bus to and from work before $\mathsf{Pr} \infty \mathsf{fWiki}$ was even thought about. As such they could do with a re-read. --prime mover (talk) 01:38, 2 October 2019 (EDT)