Negative numbers are a type of real number that is less than zero. They are represented by a "-" symbol in front of the number. Examples of negative numbers include -1, -5, and -0.25.
Negative numbers were first introduced as a concept in mathematics to solve equations that did not have a solution in the set of positive numbers. They were later proven to exist through the use of number lines and algebraic equations.
The proof of negative numbers lies in the fundamental properties of arithmetic, such as the commutative, associative, and distributive properties. These properties hold true for negative numbers, just like they do for positive numbers. Additionally, the existence of negative numbers can also be proven through mathematical induction and the use of complex numbers.
Yes, negative numbers have many real-world applications, such as in finance, where they represent debt or losses. They are also used in weather forecasting to represent temperatures below zero, and in physics to represent quantities such as velocity and acceleration in the opposite direction.
Yes, two negative numbers can be multiplied together. The product of two negative numbers is a positive number. For example, (-2) x (-3) = 6. This can be understood through the concept of multiplication as repeated addition, where the negative signs cancel out and result in a positive number.