Talk:Amenable number

Definition

The definition in the article does not agree with that of Clifford A. Pickover (2011). A Passion for Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality. John Wiley & Sons. p. 88. ISBN 1118046072. where the sum and the product have to have the same number of terms but that number does not have to be the target. So 4 = 2+2 = 2×2 is explicitly stated to be amenable. Deltahedron (talk) 09:11, 8 December 2012 (UTC)

Pickover may have gotten his definition from an earlier version of this page or an earlier version of the MathWorld page. The original definition definitely required the number of terms to be the target. Without that requirement every natural number is amenable, just use {1,1,-1,-1,n} for the natural number n. This page was rewritten when the MathWorld page was revised, but some parts of our page still reflect the older version's definition. I will attempt to straighten this out. Bill Cherowitzo (talk) 04:51, 6 August 2014 (UTC)

Question

Could this concept of "amenable number" have anything to do with the algebraic concept of "amenable group" ??

In mathematics, an amenable group is a locally compact topological group G carrying a kind of averaging operation on bounded functions that is invariant under translation by group elements. The original definition, in terms of a finitely additive invariant measure (or mean) on subsets of G, was introduced by John von Neumann in 1929 under the German name "messbar" ("measurable" in English) in response to the Banach–Tarski paradox. In 1949 Mahlon M. Day introduced the English translation "amenable", apparently as a pun.

Anyway, are these two concepts linked together ?? Or will there be nothing? — Preceding unsigned comment added by 179.178.220.101 (talk) 12:11, 26 January 2017 (UTC)