You could also invent new letters.
I’d paid to see someone try an use a sytem like that in real life! 
“That will be lalala dollars and lalalalalalalalalalala cents.”
Remember these are humans who are naming these for common use. So it needs to be something they can
A. say within their life time
B. Do the same with writing
So limiting the size of the word means all possible sound in every combination will be used and soon repeated. Any repeated number could have something to show it was a repetitions like people do with names like John IV or something like that.
You need to remember we are not able to produce an infinity number of unique sounds nor say or write for an infintiy time so if humans do the nameing then anything goes. Hey, it not to late to claim your own number!
Cek - No, no, no, no. Infinity does not mean “all possibilities and all combinations.” Perhaps a better, if not imperfect, idea would be “neverending.”
For example, let’s look at the system for naming heavy elements. Come up with any atomic number, and you will have a name which results using this formula. And no name will EVER contain any string other than the 10 letter combinations given. Sure, it ain’t practical or efficient, but for an element of theoretical atomic number 13257032 we can call it: untribipentseptniltribium. And, as a bonus, you even get the chemical symbol Utbpsntb. Even stretching this out to infinity, you will never reach a point where you will need to resort to other letters or prefixes. And you can’t, anyway, since those other letters and prefixes are outside your original definition.
I’m not fluent in set theory, so please correct me if I’m wrong, but let’s take the set of all real numbers. We can say this set is infinite, yes? How many of these numbers are negative? An infinite number. Yet the integer +5 is not included in that set, even though the set itself is infinite.
Sorry, Cek, missed your last post. But I don’t think efficiency need be discussed in this conversation, as this is more a theoretical discussion than a practical one. At any point, though, no matter what naming system you use, it will become impractical to actually say the name of that number, so I don’t think efficiency is a point here.
[Spinal Tap]
This one goes to 11.
[/Spinal Tap]
A human voice can only make finitely many sounds. In a set amount of time, these can be strung together in only finitely many permutations. So how many different numbers have a name that can be spoken in less than, say, 15 days? Only finitely many. The point being, no matter how you name them, the names of (infinitely many different) numbers will not be sayable in a lifetime (or several lifetimes).
The same with writing. No matter how you attribute words to numbers, there will be numbers with arbitrarily long names (unless you do something like invent a different letter for each number, like I mentioned above). Names that have more letters in them than there are protons in the universe.
So my “lalalala” naming system is, in the long run, no more or less inefficient than any other naming system, which would, by necessity, suffer from the same problem of having arbitrarily long names.
I’m considering that line of work. How much did you pay?
Sort of like how we run out after one hundred, and we go back to one, but add the sound “one hundred” in front of it? And again after one thousand, and after one million, and …
On the other hand, if you really want to repeat numbers, why not just use the same word for every number? Everything is so much simpler: One plus one is one. One minus one is one. One times one is one. One divided by one is one, unless one equals one, in which case it’s one.
I believe in HG2TG there is mention of the idea that if the universe is truly infinite, then everything must grow on a tree somewhere. I think, in this small way, that the HG2TG is wrong.