What is the Chinese Homophonic Group? Equivalent question: What Chinese letters won't equal 1? (If I need to specify, then I guess I'll pick Mandarin)


From: the homophonic group: a mathematical diversion
 --> This is an exercise from Michael Artin's Algebra on, well, abstract algebra. In this exercise for the English language, words are equal if they are homophones, kind of like a formalisation of the joke that sin(x)/n=6. So in English:

bee=be --> This implies e=1 by cancellation of b and e.

buy=by --> This implies u=1 by cancellation of b and y.

rase=raze --> This implies s=z by cancellation of r and e.

canvass = canvas --> This implies s=1 by cancellation of c,a,n,v,a and s. By canvass=canvas and rase=raze, we have s=z=1.

Eventually, all 26 English letters will equal 1. Apparently, this was done for French and Czech.
Chinese writing works differently, of course, to alphabetical writing.


If you define the basic unit of written Chinese as the character, then no Chinese character will equal 1, because there's no such thing as a silent Chinese character.*
If you define the basic unit of written Chinese as a stroke, then the homophonic group is trivial and is just the group comprising all strokes.
If you define the basic unit of written Chinese as all unicode-encoded decompositions (this is not a natural way of decomposing the written language), then non-1-value characters can be found by searching through a database for characters which aren't part of any other character. Examples can be found by Googling search terms like "CJKV Characters with the most strokes".


*I suppose if you wish to reduce expressions like "Aaaaah! (啊啊啊啊!)" then you could plausibly say that 啊 = 1...