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When I say "argument-based", I mean $\min$ and $\max$ functions that take arguments, as opposed to the min and max of a function. For example: $\min(3,4,-2)=-2$, $\min(100,3)=3$, $\max(3,4,-2)=4$, etc.

Now, I wish to define $\max$ and $\min$ as some formula. I have found out that $\min(x_0,\ldots,x_n)=-\max(-x_0,\ldots,-x_n)$ (after some legwork), but this is not what I am looking for.

I have been working on this problem from time to time since December 2014. I do not think I can solve this on my own (otherwise, I might have already). Is this even possible? If so, then how?

Any help is deeply appreciated.

Conor O'Brien
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    Is this what you are looking for http://math.stackexchange.com/questions/13237/arithmetic-function-to-return-lowest-in-parameter ? – Martin R Feb 22 '15 at 21:42
  • @MartinR In part, yes; I was hoping for some formula that could extend to $n$ parameters. – Conor O'Brien Feb 22 '15 at 21:46
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    Also related: http://math.stackexchange.com/questions/13253/nice-expression-for-minimum-of-three-variables. – Martin R Feb 22 '15 at 21:48

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