Hiya! Reading a lot of the comments, many of them critical of your assumptions and maths, kinda inspired me to respond. I think there were a few interesting mathematical things you did touch upon.
The number three is a “nesting” number in maths. So showing the interesting relationships that emerge by counting in 3 (instead of 1) are real mathematical relationships, and you say 1-9 is the base set of all numbers used.
Well if your using math to make a point, of course you would be mistaken, however counting math does kinda support your conclusion, paradoxically.
First, to arrive at all possible counting numbers, you don’t need 1-9 and that would be incorrect to say that. If you want to derive the rules for all counting numbers you just need three numbers, 0, 1, and 2. Only from 0,1,2 can you derive the counting numbers 1-9.
However, to your point, 0,1,2 are three numbers, the true minimum for counting numbers to exist at all.
I’m not sure how you made the leap to numbers of letters in an alphabet, im not sure how or if at all
Counting numbers evolved into letters in that order. But if they did, then you can see by counting the letters 1-9, and finding a missing letter, the missing number would obviously be “zero” the same number you left out in your count between 1-9.
0 does not mean “nothing” it means “nothing that can be counted” and the reason we need 0 as a placeholder for all counting numbers to be consistent is because numbers have to “emerge” from somewhere, and what they emerge from is infinity, or an infinite number of “1”. 1 is the only real counting number. But the entire collection of 1s is an infinite and this nonconceptual number, and that is what 0 is the placeholder for, a number that cannot be counted, infinity. “2” is just the first number that “orders” a collection of “1s” into the context of counting, a symbol for two 1s. So the counting numbers, 2-9, are sequential orders of the number 1 emerging from anywhere on an infinite number line. All numbers are infinite, there are just as many 2s as there are 3s, an infinite number.
So the basics of counting to a mathematician would be 0,1, and infinity.
If the alphabet needed a new letter to account for the discrepancy, it would be a letter for zero. But that would mean there would be a missing word, zero.
We didn’t have a word or concept for zero I think until around 1000 AD in the west, a “missing word” and therefore many many errors in our counting calculations.
Zero came late in the game in the west, but in the east they did have a “name” for the number 0 and that is Sunyata.
So you were very close in your summary even though you were having a thought experiment that went into another direction, gematria maybe.
I quite enjoyed your exploration! Thank you.