One-letter words in English language

The original question that came to my mind was "How many one-letter words are there in English language?". But of course, I did some research and found out there are three:

• A – an indefinite article
• I – the first person singular nominative pronoun
• O – an interjection, used in the translation of the vocative case of Latin, commonly used in poetry

[Wiktionary]

Wiktionary also mentions that every letter is a word (because large dictionaries list each letter as a single-letter word. Each such word is defined as a noun, denoting the letter with which it is spelled.) and adds that this blurs the use-mention distinction:

• mentioning the letter:

"Psychology" starts with a ‘p’.

• using as a word:

"Psychology" starts with a p.

On the other hand, there are sources out there that list only "a, I, O" as one-letter words or even just "a" and "I".

For example, University of Notre Dame mentions only "a" and "I" in cryptography notes.

Letters being a word seems like a bit controversial. Wikipedia explains letter as below:

A letter is a grapheme (written character) in an alphabetic system of writing, such as the Greek alphabet and its descendants. Letters broadly denote phonemes in the spoken form of the language, although there is rarely a consistent exact correspondence between letters and phonemes.

Letters may be used as words. The words a (lower or uppercase) and I (always uppercase) are the most common English letter-words. Sometimes O is used for "Oh" in poetic situations. In extremely informal cases of writing (such as SMS language) individual letters may replace words, e.g. u may be used instead of "you" in English, when the letter is pronounced as a homophone of the word.

So the questions are:

• How many one-letter words are there really?

  • Can we say that only "a" and "I" are one-letter words in the current vernacular? (Because "O" is considered archaic, though there are exceptions like our beloved "O Canada")

  • Are informal abbreviations considered as a word (like "u" for "you")?

  • Are letters words?

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_{Bonus: https://www.wordnik.com/lists/single-letter-words}