I know one bit of trivia, which is the symbol 0 is taken from the hole in the middle seat of a dhow where the mast went. Kind of figures that it should be a hole. — Wayfarer
Why would a dhow interest a mathematician? — TheMadFool
If you don't have zero than a negative number is simply a number less than one. No contradiction there. — StreetlightX
(Emphasis mine)In the Han Dynasty, the Chinese made substantial progress on root extraction and linear algebra.[2] The major texts from the period, The Nine Chapters on the Mathematical Art and the Writings on Reckoning gave detailed processes to solving mathematical problems in daily life.[3] All procedures were computed using a counting board in both texts, and they included negative numbers as well as FRACTIONS. — Wikipedia
Although the timeline is a bit fuzzy the Chinese knew about fractions which can be less than one. If they defined negative numbers simply as less than one they wouldn't have been able to distinguish fractions from negative numbers and they were clearly able to do that. — TheMadFool
My question is how can it be that the Chinese knew about negative numbers, defined as numbers less than zero, and didn't know about zero itself? — TheMadFool
Red rods represent positive numbers and black rods represent negative numbers.[7] Ancient Chinese clearly understood negative numbers and zero (leaving a blank space for it), though they had no symbol for the latter. — Counting rods
Brahmagupta's Brahmasphuṭasiddhanta is the first book that provides rules for arithmetic manipulations that apply to zero and to negative numbers.[20] The Brahmasphutasiddhanta is the earliest known text to treat zero as a number in its own right... — Wikipedia
Your use of the word 'discovered' above is questionable....maybe 'established a useful concept of' , would be more accurate. — fresco
I don't know what sort of problems the Chinese were solving when the encountered negative numbers so that's a dead-end for this discussion. — TheMadFool
Problem 8: Now sell 2 cattle and 5 sheep to buy 13 pigs. Surplus 1000 cash. Sell 3 cattle and 3 pigs to buy 9 sheep. There is exactly enough cash. Sell 6 sheep and 8 pigs, then buy 5 cattle. There is 600 coins deficit. Tell: what is the price of a cow, a sheep and a pig, respectively?
I actually find no logical connection between a dhow and mathematicians. Why would a dhow interest a mathematician? I'm genuinely interested. — TheMadFool
My question is how can it be that the Chinese knew about negative numbers, defined as numbers less than zero, and didn't know about zero itself? — TheMadFool
Personally I think zero began simply as a symbol for nothing and the rules of mathematical operations were a later development. I have no idea what the actual problems were in which zero was used as a number and not just a symbol for nothing. — TheMadFool
In my impression, the systematic use of the digit zero became a necessity with the introduction of the decimal (positional) system. For example, the number 504 has a zero in the middle, because of the mere bureaucratic-administrative formalisms imposed by the decimal place system. It only has a syntactic meaning. — alcontali
I'm guessing here so consider it carefully...I think zero as a number was born in subtraction problems where the minuend and the subtrahend are equal. — TheMadFool
↪fishfry ↪alcontali Thank you. Sorry for being lazy about this but do you have an idea about what kind of problems Brahmagupta was dealing with when he needed to formalize zero/nothing? — TheMadFool
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