In addition to what I wrote at https://news.ycombinator.com/item?id=26090146 :

The government implicitly guarantees that the USD can be used to purchase goods and services. Take a dollar bill. It has "For all debts, public and private". This is a guarantee by the government. If the USD gets outcompeted in the US, then that would make the government a liar, and thus it would use its power to make that not happen.

The government guarantees the value of fiat USD. The government has congress, police, military and nuclear weapons to back that guarantee.

Not only is it a "promise" by the government. It's also in its best interest to maintain control of monetary policy.

And also the people want it, so…

> The government implicitly guarantees that the USD can be used to purchase goods and services.

That's not backing, there's nothing that the government guarantees I am able to exchange for $1.

> Take a dollar bill. It has "For all debts, public and private".

That has a long list of exceptions. But regardless, that's not backing.

> The government guarantees the value of fiat USD.

No it doesn't, the value of USD fluctuates every minute, and goes down significantly over time.

Once upon a time you could take your dollars to the government and exchange it for a fixed amount of gold. That was backing.

Do you disagree about what would happen if the USD would be at risk of being outcompeted inside the US, or are you just arguing semantics with no connection to the real world?

(serious honest question)

The US government DOES guarantee that the USD has value. It's not something that they cannot fail at, but they do guarantee it. Cryptocurrency has no guarantee at all that it has value.

If your definition of "backing" is that you are guaranteed to be able to exchange it for something else, then cryptocurrency is truly backed by nothing, making the statement "backed by math" commonly used by bitcoin nerds complete nonsense.