1 = 0.999...

Yes. The repeating decimal 0.999... is actually equal to 1. Counter-intuitive, but nonetheless true, intuition be damned.

Don't know if I've blogged about it before here on the Hopper, but this sweetest of sweet proofs was just pointed out to me again recently. While waiting for the wife and children (one of my part-time jobs) to meet me at a restaurant, I browsed the mathemathics section of a nearby B&N bookstore. You know, where all the hot chicks hang out. Anyway, I flipped through a pocket math book on the beauty of proofs, and re-re-remembered this beauty.

Let x = 0.999...

Then 10 x = 9.999...

And 10 x - x = 9.999... - 0.999...

So 9 x = 9

Then x = 1

Ergo (whoa!) 0.999... = 1


Another way this proof is formed is this way:

1/9 = 0.111...

9 x 1/9 = 9 x 0.111...

1 = 0.999...

Whoa!

So very cool. I'll forget it in a couple of days, then stumble across it again in a year or two. Such is the curse of the Hopper.


Which reminds me –

Q: How many mathematicians does it take to screw in a light bulb?

A: 0.999...

(That last joke, fortunately, is not original to me ...)