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Referring to Mr Freeman's article in the July number of the Gazette, there can be no doubt as to the desirability of introducing these operators early in algebra. But they should be used only for the transformation of finite series. For this purpose it is never necessary to use negative powers of E and Δ. Some of Mr. Freeman's examples are considered below from this point of view
So far as addition, subtraction and multiplication are concerned, E and Δ, operating on a single definite function, combine with themselves, with each other and with constants according to the laws of algebra.
page 34 note * I prefer to start with this as the definition of Br . Using only elementary methods, we can then deduce very shortly a large number of properties of the Bernoullian numbers.