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Excerpt from Notes on Finite Differences: For the Use of Students of the Institute of Actuaries
Any quantity such as x2 which depends on x in such a manner that for each value assigned to x it takes a determinate value is called a function of x.
As another illustration of a function, consider, out of persons born alive, the number, lx, who would be living at age w on the assumption that these persons were subject to some definite law of mortality. Here for each value of 23, the age attained, we have a definite number alive at that age. The quantity is therefore, according to our definition, a function of x.
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