An Investigation of the Order of Integral Powers of Set of all Natural Numbers

This article established a fact on the order of difference of integral powers of all sets of natural numbers. The analysis was proof by use of established property of difference operator and principle of mathematical induction. The result proved conclusively that “if the elements of an arithmetic progression of set of natural numbers with positive common difference are raised to positive power k, then the k th difference is equal to the product of the common difference raised to power k (d K ) and k factorial (k!).