Hursty
Dollar bills, pound coins, whatever, fulfil the necessary functions of money, by the textbook definition:
Medium of exchange
Measure of value/Unit of account
Standard for deferred payment
Store of value
Also, the necessary characteristics
Fungible: its individual units must be capable of mutual substitution (i.e., interchangeability).
Durable: able to withstand repeated use.
Divisible: divisible to small units.
Portable: easily carried and transported.
Acceptable: most people must accept the money as payment (note that this is not true of your Dogecoins or whatever youâre pushing this week)
Scarce: its supply in circulation must be limited.
So fiat money is money, by the definition of ANY Economics textbook you would wish to read.
What you mean is fiat money has no intrinsic value, unlike gold or silver coins. It is not commodity money.