For every three place values after 999,999, there is a word. See, 1,000,000,000,000 is a trillion. The part that is important to this is the trillion part. If you kept adding place values, you could keep inventing words to say that number. For example, 1,000,000,000,000,000,000,000,000,000,000 is a nonillion. Wikipedia has a list for the names of large numbers, and it tells us how to reliably make a word for a number higher than 10^3,003. We take the amount of commas in the number and subtract 1. We will call this number x. Then, we run a calculation for 10^(3x+3). Here is an example for 10^850,266:

• Do simple algebra to find x (this is a number that can't be written out): 10^850,266 = 10^(3x+3)
• Remove the "10^" from both sides: 850,226 = 3x+3
• Subtract 3 from both sides: 850,223 = 3x
• Divide both sides by 3: 283,421 = x

Now that we have x defined, we can continue. Using the table from the Wikipedia page, we can name our number. What we need to do is concatinate prefixes together in our number. We start from right to left. We chunk x into parts (like how it is seperated by commas): 283 and 421. Starting with 283, we find the prefix for our number in order of least to greatest. 3 is "tre", 80 is "octoginta", and 200 is "ducenti". Adding this all together gives us "treoctogintaducenti". Because our number is not finished yet, and the next chunk is not 000, we chop off everything after and including the vowel at the end and add illi to the end of it. There are other rules to follow, so read the Wikipedia article if you are interested. This makes our first, finished chunk into this masterpiece, "tresoctogintaducentilli". The next chunk, 421, has us follow the same method at the begining. 1 is "un", 20 is "viginti", and 400 is "quadringenti". Adding all that up gives us another impressive string of letters, "unvigintiquadringenti". We are not done yet, because there is more left to do with this. Because this is the last chunk, and it is not 000, we have to chop off everything after and including the last vowel and add "illion". Doing all of that gives us "unvigintiquadringentillion". The last step is to simply add both of the words together. The final word we get for 10^850,226 is tresoctogintaducentilliunvigintiquadringentillion. Because we can change the x in 10^(3x+3) to any natural, non-zero number, that means that there is a word in English for every natural, non-zero number to exist. The limits of natural, non-zero numbers is another can of worms that this page will not go into, but if there is infinite natural, non-zero numbers, then that could mean there is an infinite number of words in English.

Update as of Apr 4, 2023: I think I figured out how to say it! This is my attempt: