> with a non-reversible function f into f(x) then you are losing information.

A non-reversible function f does not necessarily lose information. Some non-reversible functions, like one-way functions used in cryptography, can be injective or even bijective but are computationally infeasible to invert, which makes them practically irreversible while retaining all information in a mathematical sense. However, there is a subset of non-reversible functions, such as non-injective functions, that lose information both mathematically and computationally. It’s important to distinguish these two cases to avoid conflating computational irreversibility with mathematical loss of information.