Talk:Dyadic rational

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Ring properties[edit]

The question about ring properties: better dealt with on the localization of a ring page?

The question certainly does not belong in the article so I have deleted what properties does this ring have?. --Henrygb 23:09, 30 Apr 2005 (UTC)

Dyadic solenoid[edit]

I have added stuff about the dyadic solenoid as fitting well here, but I'm somewhat unclear about a couple of points. On the general level, Pontryagin duality interchanging direct and inverse limits: this would be OK, but I guess there is a point here, namely that the dyadic rationals must be taken with the discrete topology, and certainly not as a subspace of the real line. Also, the inverse limit could be taken either as indexed by N, or bi-infinite.

Charles Matthews 11:14, 13 Sep 2004 (UTC)

Solenoid redux[edit]

I believe that the dyadic solenoid is also a fiber bundle over a circle, with fiber that is a Cantor set. (Right?) However, the right way to write the the covering is a bit confusing.

Also, this article states the dyadic solenoid is a topological group, but the group action is a bit mysterious to me: is it really a group, or is it a topological monoid ? linas 15:08, 19 October 2005 (UTC)

There is now a solenoid group page, to which I have linked; these things are really too advanced to go on a dyadic rational page. Charles Matthews 15:14, 19 October 2005 (UTC)

If you run across references, I'd appreciate that; w/clarification of relationship to Dirichlet characters as well, and relationship to Dirichlet L-functions.linas 01:44, 20 October 2005 (UTC)

What relationship? I suppose in a sense Hecke characters might be linked, but Dirichlet characters are fundamentally just on a compact group (product of p-adic units over all p). Charles Matthews 08:28, 20 October 2005 (UTC)

Errm, I don't know. For a moment there, I had this glimpse. I'm working on it. linas 00:41, 21 October 2005 (UTC)

Solenoid again[edit]

The paragraph "The resulting topological group D is called the dyadic solenoid" does not make it clear whether D is the dyadic rationals or the dual group. Quotient group (talk) 21:52, 6 December 2009 (UTC)

Origin of the term "Dyadic rational"[edit]

This article would benefit greatly if it covered the etymology and adoption of the term. Krushia (talk) 14:14, 31 December 2012 (UTC)

The first usage I can find is in "A Closed Set of Normal Orthogonal Functions", J. L. Walsh, Am. J. Math. 1923. But Walsh uses the term (or actually the variant "dyadically rational") without explaining it, so it may well have an earlier origin than that. I don't know of a reliable source that covers this history so I am reluctant to put it in because of our rules on original research. Anyway, this article is about the concept of a dyadic rational number, not about their name, and the concept goes back to the ancient Egyptians as the article already states. —David Eppstein (talk) 23:02, 14 June 2013 (UTC)

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