merlyn wrote:There's a well accepted definition of 'unit'. The decibel like the litre is a 'Non-SI unit accepted for use with SI units'.
In the same way that the litre is built upon the metre, the Bel is built on the Neper... And it's a relative rather than absolute quantity.
If the OP's friend had been aware of that he may have realised you can't add and subtract them as you please.
Usually, you can -- that's kind of the whole point... But the context definitely matters, of course!
If I have a signal at +4dBu and make it 6dB louder, it will come out at +10dBu.
If a converter is aligned such that +4dBu = -20dBFS then if I raise the signal level by 6dB in the digital domain it will be at -14dBFS, and the D-A converter will give +10dBu...
But whatever... I'm not convinced the OP's friend was struggling with the maths. It seems to me more a misunderstanding of fundamental concepts relatesignally amid range, signal levels and noise floors!