2- All units are equal to a constant.
So, what constant is a dollar equal to which makes it a unit?
Presuming you mean the US Dollar 371 4/16th grains (24.057 grams) of Silver when it was established. This was done by taking a bunch of the silver coins then in circulation, measuring them and averaging.
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All this aside, bitcoin is a unit of account, in the same way that all other currencies are a unit of account.
Just because it's value and purchasing power change does not make this untrue. Time, date, payment, all are recorded in the block chain so it makes for a better unit of account than any other currency commonly traded.
No it isn't... UNITs are definable in objective terms and are a constant. It is puedo-unit, just like the dollar. "Currency" after 1971 became no different than collectibles. After 1971 we started measuring an opinion with an opinion.
We have been trading the equivalent of baseball cards or paintings.