To number things one by one. Counting is the difference between believing a set is complete and knowing its size.
Latin computare (to reckon, calculate), from com- (together) + putare (to think, reckon); to number things one by one, the difference between assuming a set is complete and actually knowing its size.
Latin putare is to reckon, and counting was never separate from thinking about a set as a whole — each single item is touched only so the total can be trusted afterward. A set that has not been counted can still be believed in, but it cannot yet be known.