 As a result, the use of "eventually" in this case is synonymous with the expression "for all but a finite number of terms" – a special case of the expression "for almost all terms" (although "almost all" can also be used to allow for infinitely many exceptions as well).At the basic level, a sequence can be thought of as a function with natural numbers as its domain, and the notion of "eventually" applies to functions on more general sets as well—in particular to those that have an ordering with no greatest element.More specifically, if formula_22 is such a set and there is an element formula_23 in formula_22 such that the function formula_25 is defined for all elements greater than formula_23, then formula_25 is said to have some property eventually if there is an element formula_28 such that whenever "formula_29", formula_30 has the said property.