[tolbiny]

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I was talking about American dollars, of course. I was just making an example (as if I were the mint).

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Recall though that at one point the US dollar was backed by something use full, ie. gold (or tangible if you want) and so there was a demand for it already. The process of separating the dollar from gold took ~60 years, so there was already a demand for dollars. This demand has maintained largely because oil is generally traded in dollars making it a very usable currency, hence the continued demand.
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That said, shouldn't we know exactly how much dilution is occurring on a daily basis?

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Uhhh probably. I am not sure precisely how the fed works somedays. They can manipulate the money supply by printing money straight out or they can lower interest rates, encouraging more people to take out loans and its the banks that are "printing" the money via FRL. This is (my impression) how the fed generally manages the curency rates, which is less precise than literally printing the cash.
Secondly inflation is generally measured by the CPI which is not a direct measure of the money supply. The CPI adjusts because of the money supply, but also because of new technologies and better production methods. A 3% increase in the CPI could mean a 6% increase in the money supply but a 3% decrease in prices due to increased efficiency. Hard again to peg perfectly. (This is all assuming my minimal understanding of the CPI is correct).