## What’s the Largest Number?

You don’t have to answer the title — it’s a loaded question. There doesn’t appear to be a largest number. Whatever number you think is the largest can always be multiplied by 10 to add a digit, just like the “lowest number” can always be made smaller by dividing it by 10.

I ask the question for a reason, though. In a comment to one of my math videos on YouTube, one viewer suggested that the largest number would be an infinite series of nines; and why not? Nine is the biggest digit and surely a string of them would be bigger than a string of any lesser digits. I simply didn’t know what the largest number would be, and this was as logical a guess as any.

However, when I started subtracting large numbers from smaller numbers for the purpose of my previous blog (“A Mind-Blowing Proof”), I found a pattern. The answer to “subtraction done incorrectly” was always a string of nines followed a seemingly random number — but it’s not random. If you added to this answer the actual difference between them you’d get 1000… (one followed by infinite zeroes). This was even true with .999… minus 1, assuming that the answer is what I posited it to be earlier (.00….001). In math terms, if X – Y = Z (where Y > X), Y – X + Z = 1000…. (where Y – X is subtraction done the way mathematicians would never suggest).

Why is that? My conjecture is that, if there is a largest number, 1000… is it. Why should this be so? I honestly don’t know. It just feels intuitively true, although I have no evidence, so take this conjecture with a grain of salt. It’s a good starting point for an investigation, though, and I’ll be sure to give this some more thought. I hope you’ll share your thoughts with me, too.