# Boxing Pythagoras

## More on 0.999…=1

In my last post, I discussed a particular video which I found to be more than a bit misleading. The discussion centered around a simple, but extremely counterintuitive notion of mathematics: the fact that the number 0.999…, or zero-point-nine-repeating, is equal to 1.

Well, as I mentioned, the very counterintuitive nature of the result led at least one of my readers to question its validity. As such, I thought I would lay out one proof of this concept, in order to make it easier for those who do not accept the result to pinpoint exactly where they disagree. I’ll break my proof down into numbered steps, to ease in that venture.

## The Legend of Hippasus

There was once an ancient Greek geometer named Hippasus who belonged to the Pythagorean Brotherhood. The Pythagoreans were a school of philosophers who held a special reverence for numbers and proportion. To these men, mathematics was more than just a method for quantifying and describing the world around them. The Pythagoreans held that numbers, themselves, were divine things, worthy of awe and worship. Relationships between these numbers– what we would now think of as a “proportion” or “ratio” of numbers– were intensely studied, as these proportions were thought to hold the secrets of the cosmos. If one were to divide a string according to some specific ratios, he could produce beautiful music. If one compared the proportions of two legs of a triangle, he could come to understand the remaining leg. Nothing in existence was more beautiful to the Pythagoreans than the discovery of these proportions and the properties they endowed.