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As the title says, suppose I have sets $X= \{ 1, 2, 3,10\}$ and $Y=\{199, 8\}$, then is there an accepted notation to choose $X$?

Something like: $\max_{|\cdot|}(X, Y) = X$ ?

Luce
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  • Do you mean "larger"? Because $X$ has greater cardinality than $Y$ ... (Incidentally, I don't know of any such notation.) – Noah Schweber Nov 12 '17 at 00:15
  • @NoahSchweber yes, fixed it. – Luce Nov 12 '17 at 00:18
  • You can always define such a function: $\tau(X,Y)= \left{; X,;\textrm{card}(X) \geq \textrm{card}(Y);\quad Y,;\textrm{card}(X) < \textrm{card}(Y) \right. $. But sadly, no, there is no standard notation for what you have in mind. Also keep in mind that the function would return the first set should they be equipotent. – Behemoth Nov 12 '17 at 00:37

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$\operatorname{argmax}$ is the notation you're looking for. Whereas $\max$ gives the maximum output value, $\operatorname{argmax}$ gives the input value which produces the maximum.

So you would say $\operatorname{argmax}_{S} (|S|)$.

mephistolotl
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