I have been told that .999… = 1. I don’t mean .999, but .999…, the ellipsis denoting a limitless series of nines following the decimal point. I remember somebody trying to explain this to me once. My feeling was that somewhere way at the back of the number there was a mote of a missing number, that no matter how many 9s you added to the end it still slightly defective. He said — I remember this well — he said he would explain it to me “as if I were a child.” I wasn’t a child at the time. He did some formula showing it to be so (10x – x = 9x; 9x/9 = x; do where x=.999…), but I felt like it was trickery. I’d seen a similar stunt to prove that 1=2 (never mind that one; it depends on a divide by zero error).
Nevertheless, I have come to accept that .999… = 1, because the mathematicians say so. It’s an article of faith. I recently saw mention of the fact that while many adults do know that .999… = 1, and may be able to do the mathematical computations to “prove” it, that the proofs themselves are not explanatory, they show “that” .999… = 1 in our notation, but not “why” .999…=1, which is locked up in the true meaning of infinitely repeating decimal points. The article quoted some math professor expressing frustration — that people have basically just memorized the factness of the formula, but don’t really grasp it. I imagine he loses sleep over this, that grown ups don’t get the absolute value of decimals. They insist that an infinite series is a process, their intuition is that “you keep adding nines,” but for him they are already there, all the way to the end of the universe and back. It must be a tough life, seeing all those nines when other people can’t. Even when they say “if you say so,” and accept the factology of the fact, he grimly considers that they don’t know it. Not the way he knows it.
Well, I’m part of the problem. I’ve seen and accepted the proof, but to me those nines will always be trailing along after the decimal point, trying to catch up to the numeral 1… who I’ve come to think of as glib and self-assured. Maybe it’s because I’m aware of my own perpetually dwindling non-quite-thereness. Or maybe I’m just not smart enough.