## Tuesday, June 20, 2006

Polymathematics: No, I'm Sorry, It Does.

This is an interesting item, if only because it has drug a very large number of self-professed (and denial-laden) non-math geeks out of the woodwork to complain about a simple concept. That concept is that .9 (nine repeating to infinity) = 1

The author starts out with a very elegant proof using algebra, which a lot of people will understand, and then follows it up with what I think is probably the most graspable explanation:

1/3 = .33333...

2/3 = .66666...

.33333... + .66666... = .99999...

Now, if 1/3 + 2/3 adds up to .9, and 1/3 + 2/3 adds up to 1, an infinite geometric series represented as .9 equals one.

I think that the typical naysayer is having difficulty with the concept that the infinite series doesn't end when you get tired of writing 9's, and that the number itself doesn't change just because you write more of them. Whether you write a single "9" or two million of them, the number is the same, .9 is exactly the same number as .99999999999999999999999999999999999999999999999999999, which is the same number as 1.

It's easy enough to miss thinking of it that way, though, so it quickly becomes obvious why there are a lot of people out there that have problems with the amount of imagination required to really "get" certain mathematical concepts, and why it takes a dedicated, persistent, and imaginative teacher to explain things like this.

This article has been linked to on digg.com, and the conversation thread has grown large enough to seriously slow down my browser when I try to read the page.

I have to admit that I'm pretty discouraged by the number of people absolutely denying that it can be possible (There's a warning at the top of the page that people are reporting that the information in the article is untrue!), but then again, math was always a subject that I liked, especially when I am shown something so obvious that I would intuitively argue with, if not shown a proof.

I'd like to give a heartfelt "Thank you" to Mr. Anonymous who decided to share his experience in the classroom and managed to extend it to the rest of the world.