Contrary to the stipulation that “notes shall be redeemable in lawful money on demand,” U.S. dollars are not redeemable in anything. If anyone went to the Treasury Department to unconditionally demand gold for dollars, they would find themselves handcuffed in the back of a Secret Service squad car. Dollars are basically backed by hopes—hopes that the FED will call the right shots and that the stock market won’t crash—again. The FED is known to call some shots that have figuratively taken the public from the bank to the cleaners.
The public has been unwittingly lured into a winless game of collecting non-redeemable paper currency, while the FED and the government own gold and other resources of value. Nevertheless, as long the dollar maintains its purchasing power, the average person will probably remain unconcerned about the politics of money, the dealings of the FED, and things like inflation.
Because of the balance derived from the Gold Standard, there was no such thing as inflation before the FED. In fact, the dollar was worth the same in 1913 as in 1813. Inflation (too many dollars chasing too few goods) did not exist because the circulating currency was proportioned to the value of gold.