Wikipedia:Reference desk/Archives/Mathematics/2007 October 25

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October 25

prisoner's dilemmas

where to find the 64 analyzable prisoner's dilemmas ? 71.113.165.99 11:58, 25 October 2007 (UTC)

Our Prisoner's dilemma article describes one of them, and perhaps can get you started on the search for the other 63. -- Meni Rosenfeld (talk) 12:14, 25 October 2007 (UTC)

Could someone explain the question? Are there 64 nontrivially distinct kinds of payoff matrix, or what? —Tamfang 22:16, 25 October 2007 (UTC)

Perhaps my sarcastic response's disguise as an honest answer worked too well. I had no idea what the question is about, but a google search gives some possibly relevant results, such as this. -- Meni Rosenfeld (talk) 23:03, 25 October 2007 (UTC)

I'd look in the bibliography list of the book "Moral Calculations" by Mérő László – b_jonas 16:55, 26 October 2007 (UTC)

darboux sum

how to find darboux sum of the function f(x)=x^2over the interval {0,1}??? —Preceding unsigned comment added by 86.62.27.222 (talk) 12:56, 25 October 2007 (UTC)

Did you see our article on the Darboux integral? Does the problem statement somehow specify intervals? Otherwise the problem is somewhat underspecified.  --Lambiam 19:11, 25 October 2007 (UTC)

Greater than or approximately equal to

Could "greater than or approximately equal to" be validly represented by ≈ surmounted by >, and "approximately proportional to" by ∝ surmounted by ~? Also, how would these operators be produced in LaTeX? NeonMerlin 21:13, 25 October 2007 (UTC)

What do you mean by "could"? You can use any symbol in any way you want, the question is only whether people will understand it. If you mean, "is it commonly used?", then the answer is no - I have never seen it. If you mean, "will everyone seeing it understand that this is the intention?", the answer is "possibly". If you mean, "is it acceptable to use it with an accompanying explanation", I guess than answer is yes.

I do have to wonder, though, where have you found a use for it.

Help:Formula, among other things, lists numerous LaTeX symbols. You will probably be interested in $\gtrapprox$ and $\lessapprox$. -- Meni Rosenfeld (talk) 21:30, 25 October 2007 (UTC)

I would suggest something like $A+\epsilon >B$ as an alternative to trying to say "greater than or approximately equal to". This would say the same thing without inventing new symbols while also giving you the opportunity to precisely define the amount of acceptable error ($\epsilon$, or "epsilon") for "approximately equal" if you choose to. It also demonstrates a practical way to compute the value of the expression. - Rainwarrior 08:23, 26 October 2007 (UTC)

This topic is of particularly interest for those writing TEI. It is necessary to have a way to display this particular symbol because, although it is not in common usage anymore, it has been used in the past. For example, this symbol is used throughout the Matterhorn papers at Princeton. Despite its archaic use, we still want to be able to display the the original text in the same format, but with increased legibility. Using the above method, although probably more effective, we cannot, if transcribing a document, continue to preserve the original intent of an often long deceased author.