View Full Version : 100/3 =?
One hundred, a fairly commonly known number, often the basis of mathematical equations etc. For instance the whole percentage thing is based solely on it. Yet perform a simple sum with it and the whole of maths gets thrown up in the air. This sum is, of course, the following:
100 divided by 3. (100/3)
And yes, I here you all yelling, "don't be a knit-wit, it's 33.333333recurring," but wait, say it was 33.3recurring, multiply that by 3 and you get 99.9recurring hense the answer to this puzzling question cannot be 33.3recurring. I entered 3/99.9999999 into my calculater and it came up with 3/100 so therefore calculators must recognise 99.9recurring as 100. This made me wonder whether any of maths is correct. Of course I came to the conclusion that it must be, but this was simply something I had to ignore and was the only minor error in the world of mathematics. I asked my maths teacher and he was puzzled at the question for some time and I never really got an answer. So what do you guys think about this conundrum?
Not a connundrum. 0.99recurring IS 1.0. It was always that way, it's just how maths works.
http://en.wikipedia.org/wiki/0.999...
Infinity is a strange beast.
0.9999999999......... is infinately close to 1, therefore, it must be 1. It takes some people a while to get their head around, but then again, infinity itself isn't a number, just a concept.
Not a connundrum. 0.99recurring IS 1.0. It was always that way, it's just how maths works.
Nope sorry. That is one of the most incorrect things I've ever heard you say. 0.99recurring is NOT 1.0. No matter how close the two numbers are, you cannot say they are the same. It's like saying 2 and 3 are very similar numbers, therfore they must be the same. Sorry Plasma, that's just simply not right, no matter how "accepted" it is, it will never be true.
No matter how close the two numbers are, you cannot say they are the same. It's like saying 2 and 3 are very similar numbers, therfore they must be the same.
No, no. It's not that the two numbers are really really close, therefore they must be the same; it's that the two numbers are actually the same number, just in different guises!
No, no. It's not that the two numbers are really really close, therefore they must be the same; it's that the two numbers are actually the same number, just in different guises!
NO, What are you some kind of fool or something? THEY ARE NOT THE SAME NUMBER, THEY ARE JUST VERY CLOSE!
NO, What are you some kind of fool or something? THEY ARE NOT THE SAME NUMBER, THEY ARE JUST VERY CLOSE!
Proof. (http://en.wikipedia.org/wiki/0.999#Digit_manipulation)
Moreso, REPEATING YOUR OPINION BUT THIS TIME IN ALL-CAPS does not make it any more believable.
What are you some kind of fool or something?
Gee. Nice. I answer your question and in gratitude I get flaming...
AndrewTaylor
23 May 2007, 20:34
NO, What are you some kind of fool or something? THEY ARE NOT THE SAME NUMBER, THEY ARE JUST VERY CLOSE!
You are wrong. You are entirely and completely wrong. Your position is a logical negation of the truth. In fact, the sad truth is that, since mathematics is the one thing in the entire universe about which mankind can deduce immutable and universal truths which he can then know with utter and complete certainty to be correct, it would be logically impossible to construct a statement more wrong than yours.
There are no shades of grey. There is no debate to be had.
100 / 3=3.3 rec.
3 * 33.3 rec. = 99.9 rec. = 100
End of discussion.
Literally.
Edit: If you want to argue about it, there's a page on Wikipedia dedicated to just that argument (http://en.wikipedia.org/wiki/Talk:0.999.../Arguments), although don't expect anyone there to be remotely interested in the idea either. If the mathematical proofs don't really grab you, try a wordy one: maths works if you assume 0.9 rec = 1, and as you pointed out, maths doesn't work if you assume it doesn't. So it must, because maths has to work, by long and tiresome definition.
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