Is such a task meant to be impossible? I don't even... I can assure you that it is, in fact, physically possible for a glass of milk to contain exactly 1/7 a ga

Is such a task meant to be impossible? I don't even... I can assure you that it is, in fact, physically possible for a glass of milk to contain exactly 1/7 a gallon of milk. I assume your "cleverness" is in the assertion that I cannot "prove" 1/7 of a gallon using existent tools because such tools would report the result in a base-10 decimal, which would be necessity have to be approximated because 1/7 is non-terminating in base-10. Of course, I could instead prove it by weight. Or by combining 7 such equal portions and resulting in a single gallon. The latter being an example of exactly why fractional representation of rational numbers is useful. EDIT: As an aside, by any chance are you one of the set of people who argue that .99999999... repeating infinitely is not the same value as 1? EDIT2: This just reminded me a lot of the barometer question, as I think of various ways I could demonstrate 1/7 a gallon. Of course, some things are off the table due to being a heterogeneous substance at the molecular level. Some additional options would be on the table if it were homogeneous, like water. https://en.wikipedia.org/wiki/Barometer_question https://en.wikipedia.org/wiki/Barometer_question