Some years ago a computer science guy who looked eager to pick a fight crossed my way. He asked me if I think 1 equals 0.99999... or doesn't. Notice the three dots supposed to say the nines continue infinitely. This infinite continuation is commonly abbreviated with a bar and looks like this
Searching in what was left from my 6 semesters maths I said I think so, upon which the guy looked disappointed. I figured it was the right answer - right at least for my purposes. We then had a pleasant conversation about graphic cards I believe.
Anyway, recently this question crossed my path again. It seems to have some eternal fascination, so let me just offer my take on it. The left side is the limit for n to infinity of the sum over 9 x 10-m from m=1 to n. The limit of this sum for taking n to infinity is one, according to the most straightforward proof you can think of, namely if you pick any number only an epsilon smaller than 1 there will always be an n0 such that the sum is closer to 1 than that number for all larger n. Thus, both are equal.
You find a furious discussion of the topic here.
This post was created by random association to Mark's post You can't write that number; in fact, you can't write most numbers even though you can write that number. Wishing you all a good start into the weekend!
PS: As was pointed out in the comments, Wikipedia has an excellent site on the matter.