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Is .99999 repeater 1 or .9999 repeater?
 Oct 29, 2013
 #1
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Is .99999 repeater 1 or .9999 repeater?

It is 0.9repeater.
It is not 1, it is less than 1 but this is something that I have pondered over

You can show by division that 1/3 = 0.3 repeater
double both sides and you get 2/3 = 0.6 repeater
triple both sides and you get 3/3 = 0.9repeater

3/3 = 1 0.9 repeater is less than 1

Like I said, i have pondered this question myself.

I have placed this question along with my reponse in another forum which is filled with serious mathematicians.
I will see if any of them respond.
 Oct 30, 2013
 #2
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This is the reply that I got from the other forum.
Pero (the respondant) and Wikipedia both say that 0.9repeater does equal 1.

Even fairly competent maths and science students will resist accepting 0.999... = 1 and this has been an interseting study for educational psychologists. You appear to fall into the category of those with the maths skills to prove it, but still reject it! (A little rude but true I guess)

Extract from:

http://en.wikipedia.org/wiki/0.999...

Students of mathematics often reject the equality of 0.999... and 1, for reasons ranging from their disparate appearance to deep misgivings over the limit concept and disagreements over the nature of infinitesimals. There are many common contributing factors to the confusion:

Students are often "mentally committed to the notion that a number can be represented in one and only one way by a decimal." Seeing two manifestly different decimals representing the same number appears to be a paradox, which is amplified by the appearance of the seemingly well-understood number 1.[34]
Some students interpret "0.999..." (or similar notation) as a large but finite string of 9s, possibly with a variable, unspecified length. If they accept an infinite string of nines, they may still expect a last 9 "at infinity".[35]
Intuition and ambiguous teaching lead students to think of the limit of a sequence as a kind of infinite process rather than a fixed value, since a sequence need not reach its limit. Where students accept the difference between a sequence of numbers and its limit, they might read "0.999..." as meaning the sequence rather than its limit.[36]

Many of these explanations were found by David Tall, who has studied characteristics of teaching and cognition that lead to some of the misunderstandings he has encountered in his college students. Interviewing his students to determine why the vast majority initially rejected the equality, he found that "students continued to conceive of 0.999... as a sequence of numbers getting closer and closer to 1 and not a fixed value, because 'you haven't specified how many places there are' or 'it is the nearest possible decimal below 1'".[37]

Of the elementary proofs, multiplying 0.333... = 1⁄3 by 3 is apparently a successful strategy for convincing reluctant students that 0.999... = 1. Still, when confronted with the conflict between their belief of the first equation and their disbelief of the second, some students either begin to disbelieve the first equation or simply become frustrated.[38] Nor are more sophisticated methods foolproof: students who are fully capable of applying rigorous definitions may still fall back on intuitive images when they are surprised by a result in advanced mathematics, including 0.999.... For example, one real analysis student was able to prove that 0.333... = 1⁄3 using a supremum definition, but then insisted that 0.999... < 1 based on her earlier understanding of long division.[39] Others still are able to prove that 1⁄3 = 0.333..., but, upon being confronted by the fractional proof, insist that "logic" supersedes the mathematical calculations.
 Oct 30, 2013
 #3
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This is a second response from the other site
It is looking at an extension to the idea. I found it really interesting.

I guess if we want to add 1 + 1 , we could do it ,

we can do it from LEFT to RIGHT

0.99999 ...
0.99999 ...
_____________

We start off adding the column of two 9's next to the decimal point , that gives 1.8 , then add the next column of 9's , that gives 0.18 , then add the next column of 9's , that gives 0.018 , putting it all together we can see ,

0.99999 ...
+ 0.99999 ...
______________
1.8
0.18
0.018
0.0018
+ 0.00018
_________________
1.99998

So far , just add straight down each column , no need for a 'carry' , extend this ad infinitem to get the answer which is 2.

http://www.mymathforum.com/viewtopic.php?f=8&t=43887 (This is the web address for your question on the other side)
 Oct 30, 2013
 #4
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Another proof that 0.9repeater equals 1 has been posted on the other forum,
If you are interested go to
http://www.mymathforum.com/viewtopic.php?f=8&t=43887
 Oct 31, 2013
 #5
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0
http://www.mymathforum.com/viewtopic.php?f=8&t=43887

And the proofs just keep coming

This one uses a geometric progression to prove that 0.9repeater = 1
 Oct 31, 2013

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