IRRATIONAL NUMBERS

Any number that can be written as a simple fraction, or “ratio”—that is, a/b where a and b are both integers (whole numbers)—is known as “rational.” Conversely, any number that can’t be written in this way falls into the mathematical category of “irrational.

Irrational numbers are never-ending and could in principle be written to an infinite number of decimal places.

There’s no predictable, repeating pattern to their digits

𝚛 = ∑ 𝚗ᵢ · Ⅹⁿ
	≠ 𝑎∕𝑏  :{𝑎,𝑏}⊂ℕ

Irrational numbers were discovered by Hippasus, a follower of Pythagoras, in the sixth century BC. That mathematics should behave in such an imperfect and unpredictable way was shocking to the ancient Greeks. Some authors even have Pythagoras drowning his protégé for this outrageous finding.