Thursday, July 06, 2006

Does 0.999999...=1 ????

Is this the final word on the subject???
Do you need an excerpt?
"Okay, this is going to be my last post on the topic of how .999...=1, started in this post, and continued here. I will engage in more refuting, but I have begun to see how useless the refutations are because many of the "non-believers" (and I use that word jokingly because, as I wrote here, I don't really consider it a matter of belief) don't bother to visit the refutations page or don't read it if they do. This blog has gotten over 70,000 hits since the original post was on the front page of digg. The discussion there and at numerous other small forums makes it clear that the refutations aren't being read. There have even been meta-discussions on how this fact can get a warning from digg about containing inaccurate information, even though every knowledgeable source of information agrees with me. The only reasonable criticism I found on the digg site is that this doesn't belong in the news because the proof has been around for so long that it ought not count as news. Unfortunately, enough people seem to disbelieve it that even old news needs to be explained just one more time in the hopes that a few people will come to understand the math better.
But on to the refutations. This time, I will do them in decreasing order of sophistication of the argument. This puts the most reasonable first..."
Read On

Here are some more answers: 16 answers generated in 14 mins. Thanks Rob.

1 comment:

Stephen said...

It is sad that so many people do not understand this. The equation is used to explain the correspondence of repeating decimal numbers and rational numbers. Anyone who doesn't undertand this, does not understand the difference between rational and irrational numbers in decimal notation. Unfortunately, the concept of infinity is not properly explained in math classes until Advanced Calculus, so it has to be taken on faith that decimal fractions that repeat infinitly are rational. Unless you take that definition as a sufficient definition of infitity itself, which it is.