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$A$ is a set and so is $B$.

$f$ is a function $A \to B$.

I have a math question that asks about $|f(A)|$. What does the notation $|\cdot |$ mean?

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1 Answer 1

If the elements of $ B $ are sets, then the double bars could mean cardinality (i.e. the size of the set).

If $ B $ is a set of numbers, it probably means absolute value.

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Here's the whole question: Let A = {1,2,3,...,10} and B = {1,2,3,...,7}. How many functions f: A -> B satisfy |f(A)| = 4? How many have |f(A)| <= 4? –  mimicocotopus Sep 26 '12 at 4:47
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@mimicocotopus: Here it refers to cardinality. The first question is asking how many functions there are from $A$ to $B$ that have exactly $4$ elements of $B$ in their respective ranges. The second asks how many have at most $4$ elements of $B$ in their respective ranges. –  Brian M. Scott Sep 26 '12 at 4:52
    
Ah yes, I misread the question. Here $ f(A) $ refers to the image of $ A $ under $ f $ and so the output is always a set. So in this case, the notation must mean cardinality. –  tskuzzy Sep 26 '12 at 5:25

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