# Notation from Weyl's algebraic number theory book

In Weyl's "Algebraic Theory of Numbers", which was written in 1940, there are many symbols that look handwritten, such as Fraktur (or Sütterlin, whatever you want to call it) letters for ideals. His symbol for the rational numbers looks to me like something else entirely. You can see it a few times at the start of Chapter IV:

What is that symbol?!? I suppose it should be a letter, but when I look online at samples of handwritten Fraktur nothing resembles what Weyl is writing for rational numbers. I thought maybe it could be a lower-case q, but the way it curves on the bottom is going the wrong way for it to be a convincing q.

• Even though this character turns out not to be "Sutterlin"... there is a possibly interesting fact (that I learned only recently) that also "Kurrent" (see Wiki) handwriting system apparently provided models for some of the "fraktur" symbols. – paul garrett Jan 20 at 17:26
• I believe that the symbol itself is the "handwritten" form of the now obsolete Greek letter koppa. This would be consistent with the Weyl's use of lower case and upper case Kappa to denote the extensions. "At the koppa-kappa-cabana." – Nick Jan 20 at 21:08
• @Nick the answer by kimchi lover points out that Weyl calls the symbol he used for the rational numbers "freely invented" so it is not a Greek letter. I doubt he would call a version of a Greek letter, even an obsolete one, freely invented. – KCd Jan 22 at 3:38
• @KCd Well, my reading skills fail me once again. This is becoming a regular occurrence! I actually read and upvoted kimchi's answer. Oh whoa is me. – Nick Jan 22 at 4:00

## 1 Answer

On page 10 of that book the author wrote

The most important example of a ground field is the field of common rational numbers for which I use the freely invented symbol 9...

where he uses the symbol in question instead of the 9 that I used above.

• Ah! I hadn't thought to look for the first place Weyl used the symbol in the book, since I didn't think he would actually explain where it came from (usually the origin of notation is not written out so plainly). – KCd Jan 19 at 21:28