If something is inexhaustible, there is so much of it that it can never be finished or used up. People say this about energy, patience, kindness, a supply of jokes, or — more hopefully than scientifically — a country’s resources. The word paints a well that never runs dry. In careful talk it is often a bit of an overstatement: almost nothing in the real world is truly never-ending, so you will hear it in praise (“her inexhaustible curiosity”) more than in a lab. It is the opposite of exhausted in the “used up” sense, not the “very tired” sense. Though actually, English lets exhaust do both jobs, which is why this word can feel slipperier than it looks.