Friday, September 11, 2015

Detail #204: Forming Numbers Additively and Subtractively

Let us imagine a language that forms tens up to 50 "additively" in some sense - twenty, thirty, forty and fifty derive from the numbers up to six. Sixty, seventy, eighty and ninety, however, derive from the number of tens missing: ninety is one short, eighty is two short, etc. We could derive these maybe from the ordinals, so "one short of first five" = 95.

However, let's add a complication: small negative numbers were accepted quite early as a way of expressing debts. These exceptionally enough start out as a direct offset of the first hundred numbers into the negatives. Thus -5 is "one short five". However, from the first -100 downwards, numbers are formed by putting some word amounting to "minus" before the positive number phrase.

Thus down to -100, each hundred has the same "structure" to the individual numbers, but from -100 downwards, an inverse structure obtains.

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