Files that have been compressed using the compress utility typically havethe extension.
Extensions by definitions in mathematical logic formalize the addition of new symbols by the use of a definition, more specifically in the proof theory of first-order theories. For instance, it is typical in basic set theory to use the notation "emptyset" to designate a set that is empty of members. For first-order theories, this can be accomplished by introducing the new axiom "displaystyle forall x(xnotin emptyset)forall x(xnotin emptyset)" and the new constant "displaystyle emptyset emptyset," which means "for all x, x is not a member of displaystyle emptyset emptyset." Then, as should be expected given a definition, it can be demonstrated that doing so adds basically nothing to the outdated theory.
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