On the first day, two more numbers are created: 1 = {0: } and –1 = { :0}. These two numbers arise because they are the next largest and smallest integers (respectively) on the number line.

You can see that -10 is less than -5, because it’s further away from zero on the number line. With negative numbers, as you move away from zero, the digits increase but their value decreases.

Many mathematicians take an Occam’s-razor point of view: Unless there’s a compelling reason why a number should be rational, it probably is not. After all, mathematicians have long known that most ...

The ancient scholar Hippasus of Metapontum was punished with death for his discovery of irrational numbers—or at least that’s the legend. What actually happened in the fifth century B.C.E. is ...