...seconds to thirds and fourths to fractions of a third, then thirds and fractions are cub. inches. The Rule, " The order of a product is the sum of the orders of its factors," is easily proved, eg n' V T" — RV 7 — 3R — QS'"— 9" 11"' 0 X/ - T? X m — TTT8 - <'° -Z iL...

...positive or negative integer and is called the order of D. The product or quotient of two units is a unit. The order of a product is the sum of the orders of the factors. A p-adic number D = [p*~\E is called integral if its order n is positive or zero, and...

...for big n the /-adic order of g • gn is constant. Since gr/(.4) is an integral domain, the 7-adic order of a product is the sum of the orders of its terms. In particular, ord/(//5 - fn/gn) = ord/(/ • gn - fn • g) - ord/(0 • gn) -> oo as n —...

...of these two polynomials has the property that the coefficient of Xl+] is itself regular. (In fact, the order of a product is the sum of the orders of its factors.) Thus the set of polynomials which Fraenkel uses as denominators for R(X) is a multiplicatively closed...

...2. namely All asymptotic expansions have this structure. All expansions are sums of products where the order of a product is the sum of the orders of each term in the product. So. a contribution to a term in an expansion can be identified by an integer...