 If we include negative numbers, along with positive numbers and zero, we get the full set of integers, but it took a long time to fully accept the concept of negative numbers. The ancient Greeks did not have them. The earliest written reference to negative numbers was found in a Chinese book, The Nine Chapters on Mathematical Art, written around 100 BCE. In fact, negative numbers were not fully accepted until the 19th century. After all, you can't have less than zero eggs in the basket. Here's an illustration that highlights the problem mathematicians had with negative numbers. We use this in the How Fast Is It? video book, explaining the theory behind the Michelson-Morley experiment. We have a boat in a river, traveling upstream, with a motor that can propel it at a steady speed in still water. The river is flowing in the opposite direction. The boat's home base is a known distance away. The question is, how long will it take the boat to get home? The solution is pretty straightforward. The time it takes is just a distance it has to travel, divided by the speed it is traveling. And that speed would be its velocity minus the velocity of the river. If the distance is 30 km, and the boat is running at 20 km per hour, and the current working against it is 5 km per hour, we see that the trip home will take two hours. But what if the current is greater than the speed of the boat, say 25 km per hour? Then the equation gives us negative time. Is time running backwards? Absurd. But if we apply the math to the situation we use to develop the equation, we see that a negative time simply means that the poor boat will never make it home. The river will simply continue to carry it downstream.