Negative numbers

It is known from history that negative numbers did not enjoy popularity among people: they were incomprehensible. Here with a positive number everything is always clear! Positive numbers have long been treated as "profits", and negative numbers - as "debts", "loss": who will it be nice? Only in Ancient India and China guessed instead of the words "debt of 10 yuan" write simply: "10 yuan", but draw these hieroglyphs... black ink. In Italy, usurers, giving money in debt, put before the name of the debtor the amount of debt and a dash, like our minus, and when the debtor returned the money, crossed out. It turned out something like our plus. Indeed, because the crossed out minus can be considered a plus. German scientist Michael Stiefel (1487-1567), although he called negative numbers "ridiculous numbers," but already imagined negative numbers as "less than nothing". In his book there are such entries for numbers: 0 - 2; 0 + 2; 0 to 5; 0 + 7. In 1629 A. Girard gave a geometric interpretation of what negative numbers are. He was also the first to apply the double "+" sign.

Negative numbers are the elements of the set of negative numbers that appeared in mathematics with the expansion of the set natural numbers. The main purpose of the expansion was the desire to make subtraction the same full-fledged operation as addition.

All negative numbers, and only they, are less than zero. On the numeric axis, negative numbers are to the left of zero. For them, as well as for positive numbers, an order relation is defined that allows one to compare one integer to another.

Ancient Egypt , Babylon and Ancient Greece did not use negative numbers, and if negative roots of the equations were obtained, they rejected as impossible. The exception was Diophantus, who in the 3rd century already knew the rule signs and could multiply negative numbers. However, he considered them only as an intermediate step, useful for calculating the final, positive result.