# 255 language/english/pronunciation/homophone/trivial.p

## Description

This article is from the Puzzles FAQ,
by Chris Cole chris@questrel.questrel.com and Matthew Daly
mwdaly@pobox.com with numerous contributions by others.

# 255 language/english/pronunciation/homophone/trivial.p

Consider the free non-abelian group on the twenty-six letters of the

alphabet with all relations of the form <word1> = <word2>, where <word1>

and <word2> are homophones (i.e. they sound alike but are spelled

differently). Show that every letter is trivial.

For example, be = bee, so e is trivial.

language/english/pronunciation/homophone/trivial.s

be = bee ==> e is trivial;

ail = ale ==> i is trivial;

week = weak ==> a is trivial;

lie = lye ==> y is trivial;

to = too ==> o is trivial;

two = to ==> w is trivial;

hour = our ==> h is trivial;

faggot = fagot ==> g is trivial;

bowl = boll ==> l is trivial;

gell = jel ==> j is trivial;

you = ewe ==> u is trivial;

damn = dam ==> n is trivial;

limb = limn ==> b is trivial;

bass = base ==> s is trivial;

cede = seed ==> c is trivial;

knead = need ==> k is trivial;

add = ad ==> d is trivial;

awful = offal ==> f is trivial;

gram = gramme ==> m is trivial;

grip = grippe ==> p is trivial;

cue = queue ==> q is trivial;

carrel = carol ==> r is trivial;

butt = but ==> t is trivial;

lox = locks ==> x is trivial;

tsar = czar ==> z is trivial;

vlei = flay ==> v is trivial.

For a related problem, see _The Jimmy's Book_ (_The American Mathematical

Monthly_, Vol. 93, Num. 8 (Oct. 1986), p. 637):

Consider the free group on twenty-six letters A, ..., Z. Mod out by

the relation that defines two words to be equivalent if (a) one is a

permutation of the other and (b) each appears as a legitimate English

word in the dictionary. Identify the center of this group.

-- clong@remus.rutgers.edu (Chris Long)

Continue to: