is an irrational number. Rational numbers, which include all integers and all fractions that can be expressed as ratios of integers, are the numbers we usually encounter in everyday life. Our shoe ...

This can include whole numbers or integers, fractions, rational numbers and irrational numbers. Real numbers can be positive or negative, and include the number zero. They are called real numbers ...

The whole world, they believed, could be described using rational numbers ... numbers—cannot be expressed as the ratio of two integers. But this realization is far from obvious.