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Is there a standard symbol for the maximization operator, much like μ for minimization?

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closed as not a real question by Lord_Farin, MJD, Julian Kuelshammer, Amzoti, Chris Godsil Jun 8 '13 at 14:29

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What do you mean by maximization operator? –  Levon Haykazyan Feb 22 '12 at 20:38
    
Like in en.wikipedia.org/wiki/%CE%9C_operator , except searching for the greatest natural number with a given property. –  Sam Long Feb 23 '12 at 20:49
    
How do you imagine computing that number? I believe that won't be computable. –  Levon Haykazyan Feb 23 '12 at 21:38
    
Oh, sorry, I forgot to say I'm thinking about bounded search. –  Sam Long Feb 23 '12 at 22:12
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2 Answers 2

In a comment, Carl Mummert says:

For a bounded search, we typically use would use "max".

What he means here, I think, is that if $\mu x.\Phi(x)$ denotes the minimal $x$ for which $\Phi(x)$ holds, then $\max x.\Phi(x)$ would denote the maximal such $x$.

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I'm not really sure this is pertinent to the question, but type theorists often use $μx.P(x)$ for the minimal type $x$ satisfying $P(x)$, or for the minimal fixed point of some equations, and in this context they sometimes use $\nu$ analogously for the maximal fixed point or the maximal solution.

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