For no good reason, the article of the day in Wikipedia today is about 0.999…, meaning a zero followed by a decimal point followed by an infinite series of nines. So far so good, as we’re all used to seeing, for example, one-third represented by both a fraction (e.g., 1/3) and as a similar decimally notated number (e.g., 0.333…) or some other representation, like having a bar over the last three.
But the point of the article is not to simply note that such a recurring decimal exists, but rather to also say that it is equal to one. As in:
0.999… = 1
Not that they’re just similar, or like really really close. No, not just that. But that they are in fact absolutely equal. They are two ways of representing the same number.
So at first I’m amused by such a silly notion. Then I’m a little distressed when they offer a number of mathematical proofs. (The simplest of which is starting with that 1/3 = 0.333… and then multiplying both sides by 3. Gets you there, don’t it?) So then I actually start to get slightly pissed off about it.
The article goes on to discuss the stress that math students feel about this particular concept and its proofs, so I’m not unique or anything in my reactions. But still, it’s like the stages of grief, you know, having to deal with this new fact that I really could’ve done without knowing.
And so then the only thing to do now is to burden you with it.
(And yet I’m still hoping that this is some sort of MIT or CalTech version of an April Fool’s joke.)
2 thoughts on “Well, I was on the math team in high school”
I don’t know if it’s ‘proof,’ but I’ve always looked at it this way:
X/9 = .XXX where 1
stupid html tags.
X/9 = .XXX where 1 is less than or = X is less than or = 9
where .XXX is a decimal followed by the infinitely repeating number that is X.
1/9 = .111
2/9 = .222
8/9 = .333
9/9 = .999, where any # over itself = 1
.999 = 1? No problem
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