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The number of partial functions $A \rightarrow B$ is $(1+|B|)^{|A|}.$ Now either this is a well-known formula, or I just made a mistake in the proof I just wrote. Which is it?

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Looks right to me at first glance. –  Alex Becker Feb 1 '13 at 22:31
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The formula is fine. And if your argument is to add an extra element $*$ to $B$ so that $f(a)=*$ means that $a$ is not really in the domain of $f$, then your proof is fine, too. –  Brian M. Scott Feb 1 '13 at 22:35
    
Oh, it's that easy..... :( –  goblin Feb 1 '13 at 22:35
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Nah, it's complicated, uses the binomial theorem, non-standard notation etc. I much prefer your approach! –  goblin Feb 1 '13 at 22:38
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For what it's worth, the symbol usually chosen (at least in computer science) for the extra element is "$\bot$". –  Henning Makholm Feb 1 '13 at 22:42

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