0.99999… = 1, exactly
I saw an interesting story on Digg today. It was interesting not because of the story, but because I was surprised that others found it interesting. The link was to an article claiming and proving that 0.99… (repeating nines) is equal to 1. That is, they both represent the same number.
This is a tautology that every algebra student should be able to understand.
But the comment thread on the original post is amusing. It starts out with various people claiming it’s not true, and some others showing how the commenters got it wrong. But then it devolves into several thousand comments, many with Math Majors claiming the original post is so far wrong that it’s absurd!
But it is clearly correct, and anyone who thinks otherwise simply doesn’t understand mathematical concepts.
Hey — here’s an easy problem, but with a surprising answer:
What’s are the next two numbers in this series?
142857, 285714, 428571, 571428, 714285, ??????, ??????
June 25th, 2006 at 1:51 am
the next one should be 857142 but i dont see that there is one after that unless it goes back to 142857. but i was an english major and am not much of a math whiz.
btw, thanks for the headstart on the gdata api. i was comtemplating doing just what you did (and came across this blog because i was hoping to avoid it). if i end up extending it, i will post/contribute my work.
June 26th, 2006 at 11:40 am
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Stop reading here if you don’t want to see the answer given away.
The next two numbers are 857142, 999999.
142857 + 142857 = 285714
285714 + 142857 = 428571
428571 + 142857 = 571428
571428 + 142857 = 714285
714285 + 142857 = 857142
857142 + 142857 = 999999
It turns out there’s an infinite number of series like this. I found this one by looking at sevenths. 1/7 = 0.142857(142857). 7/7 = 0.999999(999999), or 1.0. This sequence (repeating decimal) occurs for many fractions where the denominator is a prime number. I happened upon this tidbit over at Wikipedia on this page.
November 2nd, 2006 at 8:53 am
The nicest way I’ve always had of thinking about this is as follows :
1/9 = 0.11111111111111111111 etc
2/9 = 0.22222222222222222222 etc
etc
so,
9/9 = 0.99999999999999999999 etc
But 9/9 is also of course equal to 1!
QED