On Mathematical Equalities and Inequalities in the Life Table : Something Old and Something New

This paper discusses known mathematical equalities and inequalities found within lifetables and proceeds to identify two new inequalities. The first (theorem 1) is that at anygiven age x, the sum of mean years lived and mean years remaining exceeds lifeexpectancy at birth when age is greater than zero and less than the maximum lifespan.The second inequality (theorem 2) applies to the entire population and shows that thesum of mean years lived and mean years remaining exceeds life expectancy at birth.Illustrations of the two inequalities are provided as well as a discussion