# What does the notation $|f(A)| = X$ mean?

$A$ 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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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.
@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