The Instigator
Sorrow
Pro (for)
Winning
58 Points
The Contender
master98
Con (against)
Losing
5 Points

0.999999 equals to 1

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Post Voting Period
The voting period for this debate has ended.
after 12 votes the winner is...
Sorrow
Voting Style: Open Point System: 7 Point
Started: 3/24/2010 Category: Education
Updated: 6 years ago Status: Post Voting Period
Viewed: 3,998 times Debate No: 11539
Debate Rounds (2)
Comments (21)
Votes (12)

 

Sorrow

Pro

Only doing this to see who would want to accept this. Sisyphean task, step right up.

0.999999999... (repeating) = 1.
master98

Con

I would like to start by thanking my opponent. This is my first debate and I am excited to improve my skills. Now...

My opponent states that 0.9 repeating is equal to one however this is impossible, due to the fact that no matter how long the 9's may continue on for, they still do not equal one. Let me define equal, because my opponent has failed to do so.

equal: as great as; the same as
http://dictionary.reference.com...

it is impossible for something even a fraction of a decimal in DIFFERENCE from one to be equal to it. No matter how long the decimal nines continue, the 1 wll still be a very small amount larger. Regardless of whether that amount would matter to anything there is still a difference. They are separate by an infinitely small number. There is a difference.

Once again, thank you for the debate. I look forward to your counter
Debate Round No. 1
Sorrow

Pro

Errr..my opponent has forfeited as mentioned in the comment section, so I guess there's really no need for me to counter the above.

Here are some simple proofs though, in case you aren't entirely convinced (Google can help). 1/3 = 0.33333333 repeating. 3/3 = 1, but 0.333333 repeating x 3 = 0.9999999. This is where your calculator even agrees. Type in 0.99999999 with at least 20 9's (if you calculator can store that many digits) and press Enter (Equal). It'll equate to 1.

Also, many other higher-leveled mathematics have complex ways of proving this, so I'll just paste Wikipedia. Semantics is really the only argument here, albeit hitherto we are dealing with mathematical reasoning only.

http://en.wikipedia.org......
"In other words, the notations 0.999… and 1 represent the same number. Proofs of this equality have been formulated with varying degrees of mathematical rigour, taking into account preferred development of the real numbers, background assumptions, historical context, and target audience."

"The equality 0.999…=1 has long been accepted by mathematicians and taught in textbooks. In the last few decades, researchers of mathematics education have studied the reception of this equality among students. Some reject it due to their intuitions that each number has a unique decimal expansion, that nonzero infinitesimal numbers should exist, or that the expansion of 0.999… eventually terminates. These intuitions fail in the real numbers, but alternate number systems can be constructed bearing some of them out. Indeed, some settings contain numbers that are "just shy" of 1; these are generally unrelated to 0.999…, but they are of considerable interest in mathematical analysis."

I thank my opponent for the debate, and hope you all vote PRO.
Debate Round No. 2
21 comments have been posted on this debate. Showing 1 through 10 records.
Posted by omelet 6 years ago
omelet
I always laugh when I see people who strongly believe that the numbers are different, despite their complete lack of expertise in mathematics.

Here's a helpful tip: 0.000...01 is not a real number. The difference between these two numbers quite literally is zero - they are in the same exact position on the number line. The are mathematically equivalent in every single sense of the word. The fact that you feel they should be different because they look different is not a good reason to act like an authority. 2/5 looks different than 0.4, which looks different than 0.3999..., but they are all three the same number.
Posted by Puck 6 years ago
Puck
You are ignoring the infinite qualifier.
Posted by bombmaniac 6 years ago
bombmaniac
depends on your definition of troll...and it depends on your definition of equal. by the stricdefinition of equal, no they are not equal. if you have 1 million 9 hundrd thousand 9 hundred nintey nine.999 cents, you do NOT have 2 million.
Posted by Puck 6 years ago
Puck
Except it's not a convenience, it's maths. You can't say 'we can't distinguish 0.9r from one in a real number system' and at the same time decry it for being part the real number system itself. No different than detailing what is 1 part of 9 parts: 0.111r. I have 9 shiny blue cars. I give you one! You now have 1/9th of all my shiny blue cars, one car; or alternatively, you have 0.111r cars. ^^
Posted by Zetsubou 6 years ago
Zetsubou
There's also million other ways to do this.
Posted by Zetsubou 6 years ago
Zetsubou
Lol, year 8 math.

0.99999... = x

X x 10 = 10x (0.999999... x 10 = 9.99999...)

10x - x = 9x (9.99999... - 0.999999... = 9)

9 = 9x
x = 1

Stupid cheap trick when I learn't it.
Posted by chrisallen 6 years ago
chrisallen
it just is. in order to refute this claim, you are refuting either the entire framework of logic, or the entire framework of mathematics, or at best the entire framework of the system of numbers which we use. it is simply not true that 0.9 recurring and 1 are distinct things, for a multitude of reasons.

some simple ones are:
the uniqueness of limits, and the definitions of infinite series
the completeness of the real numbers
the absence of a real number between them

anyone stating that there is a difference is quite simply wrong.
and probably a troll designed to piss mathematicians like me off.
Posted by bombmaniac 6 years ago
bombmaniac
no mater how much you nitpick and say that for all intents and purposes 0.9(recurring) is 1, it still isn't. even if it is mathematically accepted as one for conveniee, it is in reality not one, and therefore con wins. i voted con. the debate was not 0.99999999999999999999(recurring) is "accepted" as one, it was
"0.999999 equals to 1". as such, con must win, because the basic premise of the debate is false.
Posted by Loserboi 6 years ago
Loserboi
LOL this was a booby trap from the start
Posted by Sorrow 6 years ago
Sorrow
CON, you forfeit? Shall I still post my argument or should I just ask them to vote for me?
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Vote Placed by Rockylightning 6 years ago
Rockylightning
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SirColton
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abard124
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Teleroboxer
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Vote Placed by pewpewpew 6 years ago
pewpewpew
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omelet
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mongeese
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