Bit of a quip but it's not based on a barter system, it's based on a debit-credit system.
Bit of a counter quip, but you cannot have a debit-credit system that really does anything without first having trade. And, trade generated using currency is not significantly different from barter. At least, not enough to pick a nit.
Currency is just glorified barter, that's where the illusion starts. Debit-credit is a rung up the ladder from currency or barter, your choice.
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