Mathematics Debate

It's been about three and a half years since I blogged a math problem, so I'm way overdue.

Today, at lunch, my wife, who's a middle school math teacher, and I had a discussion about numbers. I mentioned to her something that Dave Winer had brought to my attention, this past April:

Does 0.99999 = 1?

"No - of course they're not the same," is most everyone's initial thought. Those two numbers are close... but not equal.

But, try this proof:

Q: Does 0.33333 = 1/3?
A: Yes!

Ok, next question...

Q: Does 0.66666 = 2/3?
A: Yes, again!

So, now for the punchline:

Q: Does 1/3 + 2/3 = 1?
A: Well, yes. But...

The beauty of mathematics is even though it's an abstract field, it's a pure discipline unlike, say, computer science. The laws of mathematics are constant throughout the entire universe.

So, does does 0.99999 = 1? Unfortunately, there's no simple answer.