Olive oil is a liquid fat obtained by pressing whole olives, the fruit of Olea europaea, a traditional tree crop of the Mediterranean Basin, and extracting the oil.
In standard axiomatic set theory, by the principle of extensionality, two sets are equal if they have the same elements (that is, neither of them has an element not in the other). As a result, there can be only one set with no elements, hence the usage of “the empty set” rather than “an empty set”.
The word “virgin” indicates that the olives have been pressed to extract the oil; no heat or chemicals have been used during the extraction process, and the oil is pure and unrefined.
First cold pressed means “that the fruit of the olive was crushed exactly one time – i.e., the first press. The cold refers to the temperature range of the fruit at the time it is crushed”.