Whenever there are three or more summands and at least one is a product, parenthesization starts by separating the summand with the largest numerical value from the rest. The same rule then applies to the remainder, if it consists of more than the summands, and so on.
Standardized
In numeral systems, IF there are three or more summands and at least one is a product, THEN parenthesization starts by separating the summand with the largest numerical value from the rest. The same rule then applies to the remainder, if it consists of more than the summands, and so on.
1. For example, in English, 3,423 is built with the summands 3×1000, 4×100, 2×10, and 3, since at least one summand is a product, the generalization applies. Since 3000 is the largest numerical value, it is parenthesized (3×1000) + ((4×100) + (2×10) +3). Then it is parenthesized with the second member: (4×100) + ((2×10) +3). Since the remainder has only two summands, the process is complete.The proviso that at least one of the sums is a product is made for the following reason: there are instances like Welsh (Celtic, Indo-European)“dau ar bum-theg” ‘two on five-ten’, i.e. 2+(5+10), which grouping clearly does not involve taking the largest value first. 2. In order to express the additional regularities regarding the free variation interval, Greenberg suggests reformulating this generalization into two more precise statements; cf. ##538, 539.
1. For example, in English, 3,423 is built with the summands 3×1000, 4×100, 2×10, and 3, since at least one summand is a product, the generalization applies. Since 3000 is the largest numerical value, it is parenthesized (3×1000) + ((4×100) + (2×10) +3). Then it is parenthesized with the second member: (4×100) + ((2×10) +3). Since the remainder has only two summands, the process is complete.The proviso that at least one of the sums is a product is made for the following reason: there are instances like Welsh (Celtic, Indo-European)“dau ar bum-theg” ‘two on five-ten’, i.e. 2+(5+10), which grouping clearly does not involve taking the largest value first. 2. In order to express the additional regularities regarding the free variation interval, Greenberg suggests reformulating this generalization into two more precise statements; cf. ##538, 539.