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Sharp as mathematics

> can people give me examples of the musical sharp sign used in math
> documents

Sometimes $f^\sharp$ will be used to in categorical constructions derived
>from a morphism $f$. I can probably hunt up a real live example if it
is important.

The hash mark # (this is the thing above the three on my keyboard; is it
still an octothorpe after crossing the Atlantic?) is, of course, very
commonly used for set cardinality. It is called the pound symbol in
North America (don't blame me; I'm just the messanger). I've never
seen the currency symbol used in mathematics.

It has become common to used something like $K_{i=1}^\infty$ for continued