Bart Dale said:

As can be seen, the medieval Europeans did not think negative numbers were absurd until 17th century. They were aware of them in the 15th century, and found practical applications by the 15th century, during the middle ages as a matter of fact. (It meets the 1500 cutoff commonly used for the middle ages). One ancient Greek did think negative numbers were absurd, but that did not mean all of them did as you claim. Please provide evidene for more than just one Greek who though negative numbers were absurd.

*In the 16th century, even such prominent mathematicians as Cardano in Italy, Viete in France, and Stifel in Germany rejected negative numbers, regarding them as "fictitious" or "absurd". When negatives appeared as solutions to equations, they were called "fictitious solutions" or "false roots". But by the early 17th century, the tide was beginning to turn. As usefulness of negative numbers became too obvious to ignore, some European mathematicans began to use negative numbers in their work. Nevertheless, misunderstanding and skepticism about negative quantities persisted..... Early in the 17th century, Descartes called negative solutions (roots) "false" and solutions involving square roots of negatives "imaginary"..... John Wallis claimed that negative were larger than infinity. -*Math Through the Ages

Bart Dale said:

PS - I asked you for a practical application the ancient/medieval Chinese found for negative numbers. Please provide me with that.

It says:

*In 200 BCE the Chinese number rod system (see note1 below) represented positive numbers in Red and Negative numbers in black. An article describing this system can be found here . These were used for commercial and tax calculations where the black cancelled out the red. The amount sold was positive (because of receiving money) and the amount spent in purchasing something was negative (because of paying out); so a money balance was positive, and a deficit negative.*

The concept also appeared in Astronomy where the ideas of 'strong' and 'weak' were used for approximating a number from above or below. For example approaching 5 from above means for example, starting with 5.2 you can find better approximations 5.1, 5.05, 5.025. Thus 5.025 was called a 'strong' approximation and a number like 4.9 'weak'. So 'strong' numbers were called positive and 'weak' numbers negative

The concept also appeared in Astronomy where the ideas of 'strong' and 'weak' were used for approximating a number from above or below. For example approaching 5 from above means for example, starting with 5.2 you can find better approximations 5.1, 5.05, 5.025. Thus 5.025 was called a 'strong' approximation and a number like 4.9 'weak'. So 'strong' numbers were called positive and 'weak' numbers negative

Also I said that my given list of inventions "tend" to affect farmers more, why are you focusing on only one in that list?

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