Talk:Sprague–Grundy theorem

Problems with this page:

(1) The Lemma needs cleaning up.

(2) Ideally, all of the information in the section called 'Definitions' should be removed and merged with what's in the Wikipedia entry 'Combinatorial Game Theory'. At present, however, the latter page doesn't entirely encompass what's needed for this page.

(3) The "Proof" part mixes TeX with the non-TeX math that preceded it.

Example

This article would make a lot more sense if it were expanded by including an example, for example the game of Kayles.

Huh?

I thought to add credence to the calls for a clean-up by conveying a neophyte's confusion. The article includes the text:

A nimber is a special game denoted *n for some ordinal n. We define *0 = {} (the empty set), then *1 = {*0}, *2 = {*0, *1},

So, first we are told that *0 indicates a game; next we learn that *0 represents the empty set (that is, something completely different, i.e. not a game at all). Immediately thereafter, we are told that *1 is the set of empty sets. This is rather confusing, but I think that the set of empty sets must be the empty set itself (as there is only one empty set). So that *1 should equal *0 and so on for all *n. Not only is the connection with games rather obscure, but the definition appears sterile, or, well, empty.

Who can help? --Philopedia 20:41, 19 October 2007 (UTC)

It's not "something completely different"; just before the part you quoted, we see An impartial game can be identified with the set of positions that can be reached -- so we already have the correspondence between a game and a set. *0, the empty set, is the game with no options: if it's your turn, you lose! As for *1, you're confusing the levels. There is indeed only one empty set, and hence *1 has only one element. *1 contains the empty set, but *0 is the empty set, so they're different. Joule36e5 (talk) 02:54, 25 September 2008 (UTC)

Lemma, Proof and typographical conventions

The reason that the typographical conventions in mathematical texts have been arrived at is that they make the meaning clear. In the current context, the statement of the Lemma in the section entitled "Lemma" is in no way distinguished from the rest of the section. This makes it difficult to realise the author's intention. Similarly, the section entitled "Proof" should make it clear what it is a proof of (the Sprague-Grundy theorem).

This is messy

Indeed a mathematician can define an impartial game as a set of sets that are in turn sets of sets. However this introduction totally messes things up. Informal games, games and positions are all mixed up. A glaring mistake is that once we have given a mathematical definition (or something that can be molded into such) of a "game" as "something that is guaranteed to end" (plus other properties), as we have done here, we can no longer use chess, or tictactoe as examples of "games". The definition of equivalence uses a mathematical trick that is hard to fathom. In a mathematical context, I would for novice mathematicians, I would derive a few lemma's such as that in the end an impartial game is a set with no real content (only consisting of empty sets in the end), and then just say that informally defined games result in "set definitions" that are just the same, as a set. — Preceding unsigned comment added by 80.100.243.19 (talk) 17:37, 30 October 2012 (UTC) .

Some cleanup enacted; please check

I made some drive-by edits, which happened to address some of the concerns listed here. However, I am not a game theorist, so someone should look them over. 98.16.181.175 (talk) 01:37, 14 April 2014 (UTC)

Oh! Also, why does the theorem name use an en-dash rather than a hyphen per normal typographical conventions? 98.16.181.175 (talk) 01:40, 14 April 2014 (UTC)

The standard typographical convention is to use a hyphen in the middle of a single person's hyphenated name, and an en-dash to separate two names. That way you can tell those two kinds of dash apart. For instance the Birch–Swinnerton-Dyer conjecture is named with an en-dash separating Birch's name from Swinnerton-Dyer's hyphenated name. See MOS:DASH. —David Eppstein (talk) 04:11, 14 April 2014 (UTC)

Too Technical

Hi, I realise this article covers a specialised and technical topic, however it should be noted that the article is currently hard to understand for the average reader (or maybe I'm just thick!). Please refer to item 7 in WP:NOTJOURNAL. Perhaps some diagrams and using less technical language would help its accessibility? Regards, 1292simon (talk) 02:44, 8 June 2014 (UTC)

I don't believe you are thick, and I believe that the trouble starts out of the starting block with the first sentence, ending in whatever a "nimber" is. I realise the word "nimber" is linked to its definition, but even its definition is understandable only to anyone who has played the game "nim". I have only heard of the game, but have never played it nor know its terminology. It was hard to keep reading after that. There had to be a better way to start off the article. The above reference stating that Wikipedia is not a scholarly journal is well worth reading. Paul E J King (talk) 15:17, 24 August 2020 (UTC)

I tried copyediting the lead to make it less technical by using numbers (the size of the equivalent nim-heap) instead of nimbers (the value of that equivalent nim-heap) to start out. But I soon realized that it only helps a little, because even doing it that way needs the ordinal numbers, which are still pretty specialized and technical. —David Eppstein (talk) 17:23, 24 August 2020 (UTC)