99 Bottles of Beer
Encyclopedia
"99 Bottles of Beer" is a traditional song
Song
In music, a song is a composition for voice or voices, performed by singing.A song may be accompanied by musical instruments, or it may be unaccompanied, as in the case of a cappella songs...

 in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

 and Canada
Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...

. It is popular to sing on long trips, as it has a very repetitive format which is easy to memorize, and can take a long time to sing. In particular the song is frequently sung by children on long bus
Bus
A bus is a road vehicle designed to carry passengers. Buses can have a capacity as high as 300 passengers. The most common type of bus is the single-decker bus, with larger loads carried by double-decker buses and articulated buses, and smaller loads carried by midibuses and minibuses; coaches are...

 trips, such as class field trips, or on Scout
Boy Scout
A Scout is a boy or a girl, usually 11 to 18 years of age, participating in the worldwide Scouting movement. Because of the large age and development span, many Scouting associations have split this age group into a junior and a senior section...

 and/or Girl Guide outings. The song is derived from the English "Ten Green Bottles
Ten Green Bottles
Ten Green Bottles is a song for children that is popular in the United Kingdom. In essence the song is a single verse repeated, each time with one bottle fewer:...

".

The song's simple lyrics are as follows:


Ninety-nine bottles of beer on the wall,
Ninety-nine bottles of beer.


Take one down, pass it around,
Ninety-eight bottles of beer on the wall.


The same verse is repeated, each time with one fewer bottle. The song is completed when the singer or singers reach zero.

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
    The Song That Never Ends
    "The Song That Never Ends" is a self-referential and infinitely iterative children's song. The song is a single verse long, written in an infinite-loop motif in a march style, such that it naturally flows in a cyclical fashion, repeating the same verse over and over. It is very popular with...

    ).
  • "Aleph-Null
    Aleph number
    In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality of infinite sets. They are named after the symbol used to denote them, the Hebrew letter aleph...

     bottles of beer on the wall". Aleph-Null is the size of the set of all natural number
    Natural number
    In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...

    s, 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
Continuum hypothesis
In mathematics, the continuum hypothesis is a hypothesis, advanced by Georg Cantor in 1874, about the possible sizes of infinite sets. It states:Establishing the truth or falsehood of the continuum hypothesis is the first of Hilbert's 23 problems presented in the year 1900...

, among others.

On an episode of Malcolm in the Middle
Malcolm in the Middle
Malcolm in the Middle is an American television sitcom created by Linwood Boomer for the Fox Network. The series was first broadcast on January 9, 2000, and ended its six-and-a-half-year run on May 14, 2006, after seven seasons and 151 episodes...

, on a way to the mathematics competition Macolm'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.

External links

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