This post concerns the weirdest, and possibly the coolest, thing I ever learned when studying math in high school and briefly in college.
Did you all know that the number 1 equals the repeating decimal 0.999...? Or, another way of saying it, did you know that the repeating decimal 0.999.... denotes a real number equal to 1?
I'm not making this up. For a more detailed (and better) explanation, check out the wiki article.
If you haven't clicked through to the link yet, here's the short-hand explanation.
1/3 = 0.333...
3 x 1/3 = 3 x 0.333...
Thus,
1 = 0.999...
Yikes.
You may be asking why I'm writing about this. Truth be told, I've always been fascinated by this "problem," and I encountered it recently during some research I was doing for a sci-fi novel. I won't begin to try and explain the real-world ramifications of this wonderful puzzle. As a matter of fact, I'm not sure there are any. What could it mean? Is this a problem inherent in our base-10 system of mathematics, or would this appear in all mathematical systems?
It's always cool to reexamine things taken for granted in a new light. Good fiction does this in many ways, one of them being the plot twist. A good plot twist is a plausible turn of events that forces us to reevaluate everything we've seen.
Still though, it's just crazy to think of the number 1, one of the very first things we learn, as being the same as 0.999...
6 months ago
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