Get to know rational and irrational numbers with this amusing, animated TED Ed video. You will find it useful for your GMAT or GRE preparation.
The video discusses the history and maths behind irrational numbers.
Like many heroes of Greek myths, the philosopher Hippasus was rumoured to have been mortally punished by the gods. But what was his crime? Did he murder guests or disrupt a sacred ritual? No, Hippasus’s transgression was a mathematical proof – the discovery of irrational numbers.
The discovery of irrational numbers
Hippasus belonged to a group called the Pythagorean mathematicians who had a religious reverence for numbers. They even had a dictum saying: “All is number”, which suggested that numbers were the building blocks of the universe. Part of this belief was that everything from Cosmology to Metaphysics and Morals followed eternal rules describable as ratio of numbers.
What are irrational numbers?
In mathematics, an irrational number is a real number that cannot be expressed as a ratio of integers, i.e. as a fraction. Therefore, irrational numbers, when written as decimal numbers, do not terminate, nor do they repeat. For example, the number π starts with 3.14159265359, but no finite number of digits can represent it exactly and it does not end in a segment that repeats itself infinitely. The same can be said for any irrational number.
What are rational numbers?
In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q. The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number.
Hippasus’s discovery revolutionised mathematics. So, whatever the myths say, do not be afraid to explore the impossible. Enjoy watching and do not forget to comment!