Because every transcendental number is irrational, any proof showing that pi is transcendental also proves that pi is irrational. — Will we ever have quantum laptops? — Who was the first cyborg?

The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, connects quantum ...

Rational numbers can be fractions of integers. Irrational numbers cannot be expressed as ratios. Decimal representations help identify them. Pi and Euler's number are irrational.

After an infinite number of days, all kinds of numbers are created, from fractions to irrational numbers to infinities and infinitesimals. Credit: Lukáš Lánský/Wikimedia Commons (CC BY-SA 3.0) ...

IN the first of these tracts Prof. Dedekind gives a theory of irrational numbers and of the arithmetical continuum which is logically perfect, and in form, perhaps, more simple and direct than any ...