99 Bottles of Beer - Mathematically Inspired Variants

Mathematically Inspired Variants

Donald Byrd has collected dozens of variants inspired by mathematical concepts and written by himself and others. (A subset of his collection has been published as Byrd (2010, September).) Byrd argues the collection has pedagogic as well as amusement value. Among his variants are:

• "Infinite bottles of beer on the wall". If one bottle is taken down, there are still infinite bottles of beer on the wall (thus creating an unending sequence much like "The Song That Never Ends").
• "Aleph-Null bottles of beer on the wall". Aleph-Null is the size of the set of all natural numbers, and is the smallest infinity and the only countable one.
• "Uncountable bottles of beer on the wall". An uncountably infinite set is larger than a countable one; therefore, if only a countable infinity of bottles fall, an uncountable number remains.

Other versions in Byrd's collection involve concepts including geometric progressions, differentials, Euler's identity, complex numbers, summation notation, the Cantor set, the Fibonacci series, and the Continuum Hypothesis, among others.

On an episode of Malcolm in the Middle, on a way to the mathematics competition Malcolm's classmates - the Krelboynes - sing a variation of this song stating "the square root of (number) of bottles of beer". Malcolm states to the camera that they are only at the nineties.