I have recently been involved in a discussion with someone who doesn't accept that lossless compression is possible, even in principle. This person considers himself to be technically literate, and an expert in his field of audio engineering.
I and several others have patiently tried to explain how lossless compression is possible, using simple examples such as run-length encoding and delta encoding, but he refuses to believe that it's possible for a lossless audio codec such as FLAC, for example, to exactly reproduce the input bitstream from the raw PCM data.
His response is always along the lines of:
it's getting smaller, so it must be losing data
"lossless" is just a buzzword used by software companies to sell their software, it doesn't actually mean lossless
Are there any other examples I can use to demonstrate conclusively that lossless compression is actually possible?