There is a difference between inflation and price inflation. Inflation refers to an increase in the money supply, which subsequently affects price levels, leading to price inflation. The term "inflation" has been misconstrued, leading people to believe that the fruit and vegetable vendor is to blame when, in reality, it is the government increasing the money supply and causing more money to chase the same amount of goods (resulting in price inflation). This is the root cause that Keynesians ignore, attempting to fix a hangover with more alcohol.
To measure a unit, the measurement tool must be fixed (e.g., kg, cm, L). How can you measure inflation using a fluctuating dollar? It's like trying to measure an oval with rubber bands. Inflation is a vector, with each item having its own price inflation, making it impossible to aggregate into an ever-changing CPI basket. Welcome to the fiat standard.