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So is it impossible to retrieve Bitcoins from the bill?

As I understand it, their nominal value is fixed (unchangable) - just like cash money. That way they cannot be devaluated.

If you do not have the private key they are not your bitcoins. no matter what sort of paper you have

Thats just a point of view: If you receive a 100$ Bill without any key, is it yours or is it not?

A $100 bill is the key to fiat cash, A piece of paper that says "1 bitcoin" with no way to control 1 bitcoin, is worth 0 bitcoins.