Yes. I think this is probably the only really correct answer. Dollar is in the head.

I would add that not only now, but also in the future. When there was a parity between euro and dollar, one euro could buy you one dollar, but it was not a dollar.

And physical bills might not be available, it's not a question of value, but liquidity. In Panama or Argentina, papers with dead us presidents are in short supply and people have to use another forms of usd.

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Well I added the "including a dollar bill" because Applebee's gift cards can't buy you dollar bills. A dollar in bank account that can withdraw a dollar from an ATM is a dollar.

The temporal axiom you add probably completes the definition, I hadn't considered that when answering your question.