| Elements of [math]\displaystyle{ N }[/math]
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Elements of [math]\displaystyle{ M }[/math]
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Any [math]\displaystyle{ f }[/math]
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Injective (1-1) [math]\displaystyle{ f }[/math]
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Surjective (on-to) [math]\displaystyle{ f }[/math]
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| distinguishable
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distinguishable
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[math]\displaystyle{ m^n\, }[/math]
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[math]\displaystyle{ \left(m\right)_n }[/math]
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[math]\displaystyle{ m!S(n, m)\, }[/math]
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| indistinguishable
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distinguishable
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[math]\displaystyle{ \left({m\choose n}\right) }[/math]
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[math]\displaystyle{ {m\choose n} }[/math]
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[math]\displaystyle{ \left({m\choose n-m}\right) }[/math]
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| distinguishable
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indistinguishable
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[math]\displaystyle{ \sum_{k=1}^m S(n,k) }[/math]
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[math]\displaystyle{ \begin{cases}1 & \mbox{if }n\le m\\ 0& \mbox{if }n\gt m\end{cases} }[/math]
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[math]\displaystyle{ S(n,m)\, }[/math]
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| indistinguishable
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indistinguishable
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[math]\displaystyle{ \sum_{k=1}^m p_k(n) }[/math]
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[math]\displaystyle{ \begin{cases}1 & \mbox{if }n\le m\\ 0& \mbox{if }n\gt m\end{cases} }[/math]
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[math]\displaystyle{ p_m(n)\, }[/math]
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