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It is often suggested the money fulfills several functions, including being a store of value, a medium of exchange and a unit of account.

However, I am not sure if the implication here is that money needs to fulfill all 3 functions to be considered money, or if fulfilling one or two suffices.

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According to general literature, yes it should satisfy all three. For example, some papers question whether bitcoin is money because of being poor medium of exchange such as Yermack (2015). In standard textbooks such as Mankiw's principles of economics it is mentioned that money satisfy all three functions, and you will find that in any textbook.

This being said, some of these characteristics are on the spectrum. For example, different currencies store value differently at different points in time. There is for sure some grey area there. Also, arguably the most important one is unit of exchange, since if you quote prices in terms of something then you are already ticking the box for unit of account, and store of value is often on a spectrum.

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