Negative number

A negative number is a real number that is less than zero. In mathematics, it is the opposite of a positive real number. These numbers are essential for representing a deficiency, a loss, or an opposite direction. For example, if you have a debt, you can think of that debt as a negative asset. Negative numbers are often written with a minus sign (–) in front of the digit. This symbol can represent a unary operation, which means it changes a positive number into its opposite. It can also represent a binary operation, which is the process of subtraction.

To understand how these numbers behave, mathematicians often use a number line. On this line, zero acts as a neutral center point. Positive numbers are located to the right of zero, while negative numbers are located to the left. The position on the line tells you the value of the number. Numbers that appear farther to the right are greater than those to the left. This creates an interesting rule for negative values. A negative number with a larger magnitude is actually considered a smaller value. For instance, negative ten is less than negative three, even though ten is a larger magnitude than three.

Negative numbers appear in many different types of mathematical sets. The set of integers includes all whole numbers, their opposites, and zero. Within this group, we can distinguish between positive and negative signs. Every real number except zero is either positive or negative. We use the term "non-negative" to describe numbers that are either positive or zero. Similarly, "non-positive" refers to numbers that are either negative or zero. While most people view zero as neutral, the French convention considers zero to be both positive and negative.

History shows that the concept of negative numbers took a long time to accept. Early mathematicians like Diophantus considered negative solutions to be "false" or absurd. However, negative numbers appeared in the Chinese text *Nine Chapters on the Mathematical Art* during the Han dynasty. Around the 3rd century, Liu Hui established rules for adding and subtracting them. By the 7th century, Indian mathematicians like Brahmagupta were describing their use. Later, Islamic mathematicians developed rules for multiplying negative numbers and solving equations with negative coefficients. Even Western mathematicians like Leibniz used them in calculations while still holding that they were invalid.

We see negative numbers working in science and geography every day. On a thermometer, they represent temperatures colder than zero degrees Celsius or Fahrenheit.

In geography, they describe latitudes south of the equator or elevations below sea level. Electrical circuits also use them, such as when a battery is connected in reverse polarity. In physics, ions can carry either a positive or a negative electrical charge.

In the world of finance and sports, negative numbers provide vital information. In bookkeeping, debts are sometimes shown as red numbers or placed inside parentheses. A negative balance in a bank account represents an overdraft, while negative GDP growth can indicate a recession. Sports fans use them to track differences in scoring. In association football or hockey, teams have a goal difference. In Formula 1 racing, a negative lap time means a driver was faster than the previous lap.

Even in elevators, negative numbers can represent floors located below the ground level.

Arithmetic follows specific laws to ensure that the concept of an "opposite" remains logical. When you add two negative numbers, it is like combining two debts into one larger debt. Subtraction can also produce a negative result if you subtract a larger number from a smaller one. Multiplication follows distinct rules regarding signs. The product of one positive and one negative number is always negative. However, the product of two negative numbers is always positive. This can be visualized as a change in direction along a vector.