Just saw a nice post at another math blog called Polymathematics about something that bugs me too… The way that people don’t understand what repeating decimals mean. In particular, the way that people will insist that 0.9999999… != 1. As a CS geek, I tend to see this as an issue of how people screw up syntax and semantics.
And it has some really funny stupidity in the comments. 0.9999999… = 1.
One quick quote from the post, just because it’s a nifty demonstration of the fact which I’ve not seen before: (I replaced a GIF image in the original post with a text transcription.)
Let x = 0.9999999…, and then multiply both sides by 10, so you get 10x = 9.9999999… because multiplying by 10 just moves the decimal point to the right. Then stack those two equations and subtract them (this is a legal move because you’re subtracting the same quantity from the left side, where it’s called x, as from the right, where it’s called .9999999…, but they’re the same because they’re equal. We said so, remember?):10x = 9.99999999... - x = 0.99999999... ------------------------- 9x = 9
Surely if 9x = 9, then x = 1. But since x also equals .9999999… we get that .9999999… = 1. The algebra is impeccable.
I also need to quote the closing of one of the comments, just for its sheer humor value:
Bottom line is, you will never EVER get 1/1 to equal .99999999… You people think you can hide behind elementary algebra to fool everyone, but in reality, you’re only fooling yourselves. Infinity: The state or quality of being infinite, unlimited by space or time, without end, without beginning or end. Not even your silly blog can refute that.