Talk:Vorlesungen über Zahlentheorie

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Problem with editions, there are three editions

This is a nice start to an article. Perhaps this will be of assistance to someone doing further development of it. The upshot is that Stillwell's translation is apparently on the 1st or 2nd editions, and there's a 3rd edition of 1879 that contains new material. I've cc'd the following over from a debate on the talk page re the generalized notion of "function" (I've cc'd all of this for background):

RE: Dedekind's notion of "function"

(Notice the * footnote in the following, and the word "law"). Dedekind has become a favorite of mine, in particular his 1887 Nature and Meaning of Numbers, Dover Publications, Inc, NY, ISBN 0-486-21010-3, also this is in the public domain at http://books.google.com/books?id=PywPAAAAIAAJ&printsec=frontcover&dq=Dedekind+The+Nature+and+Meaning+of+Numbers&hl=en&sa=X&ei=owdFT_HjHaTx0gG-0Nn2Aw&ved=0CDYQ6AEwAA#v=onepage&q=Dedekind%20The%20Nature%20and%20Meaning%20of%20Numbers&f=false .(I mark up my books so I paid $8.95 for the facsimile). Here is his definition in II. TRANSFORMATION OF A SYSTEM:

"21. Definition.* [*See Dirichlet's Vorlesungen uber Zahlentheorie, 3rd edition, 1879, § 163.] By a transformation [Abbildung] φ of a system S we understand a law according to which to every determinate element s of S there belongs a determinate thing which is called the transform of s and denoted by φ(s); we say also that φ(s) corresponds to the element s; that φ(s) results or is produced from s by the transformation φ, that s is transformed into φ(s) by the transformation φ" [etc. What follows is a difficult further elucidation that relies upon his notions developed earlier about T being a part of S, etc] (Page 50 in the Dover edition facsimile of the Open Court Publishing Company's edition of 1901)

This warrants more research. Bill Wvbailey (talk) 15:40, 22 February 2012 (UTC)[reply]

Interesting. With Dirichlet Vorlesungen_über_Zahlentheorie Selfstudier (talk) 16:25, 22 February 2012 (UTC)[reply]

RE Dirichlet and Dedekind -- There's a translation into English, but damned if it doesn't end at §144; the section referenced by Dedekind is from the 3rd edition at §163! Translator John Stillwell must have used the 1st or 2nd edition (ouch! cf the wiki article Vorlesungen_über_Zahlentheorie there is an issue here). Bill Wvbailey (talk) 23:06, 22 February 2012 (UTC)[reply]

--- Bill Wvbailey (talk) 01:27, 23 February 2012 (UTC)[reply]