Is 1/3 = 1
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after 1 vote the winner is...
lannan13
Voting Style:  Open  Point System:  7 Point  
Started:  4/24/2014  Category:  Education  
Updated:  2 years ago  Status:  Post Voting Period  
Viewed:  708 times  Debate No:  53256 
Debate Rounds (3)
Comments (10)
Votes (1)
Suppose this was not the case, i.e. 0.9999... != 1. Then 0.9999... < 1 (I hope we agree on that). But between two distinct real numbers, there's always another one (say x) in between, hence 0.9999... < x < 1.
The decimal representation of x must have a digit somewhere that is not 9 (otherwise x == 0.9999...). But that means it's actually smaller " x < 0.9999..., contradicting the definition of x. Thus, the assumption that there's a number between 0.9999... and 1 is false, hence they're equal. Contention 1: 1/3<1 Let's do some comparisons. 1/3 as a fraction, is equal to .333 repeating. Assuming that we are only using real number and not the imgainary number i. 1 is indeed =1. Let's apply this to real life. I have 1 pizza and I have to split it between my two friends and I. I would only get 1/3 of the pizza and not the entire pizza. My friends would 2/3 of the pizza which is .667. The two would =1. The reason for this is that we have to consider the appropriate number of significant figures. (http://www.chem.sc.edu...) You see at the end of the allotted significant figures one must round up the last digit. so indeed .9999 repeating would =1 due to the sig fig rule, but the resolution is weather or not .333=1. I have shown through the significant figures rule that indeed it would not. as .333 would not be able to round up to even .334, as 3<5 so .333 would remain as .333 and as a fraction .333 would be 1/3 of the whole number of 1. 

chilli0919 forfeited this round.
All points extended. 

chilli0919 forfeited this round.

1 votes has been placed for this debate.
Vote Placed by ESocialBookworm 2 years ago
chilli0919  lannan13  Tied  

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Reasons for voting decision: Obvious winner is lannan13. No questions asked.
Conduct: FF,
Args: his made more sense.
E.g. 0.4, 0.45, 0.5, etc.
I can understand both sides of the argument of how 0.999 ... = 1, but Pro is arguing for 1/3 = 1, or that 0.333 ... = 1.
There are an infinite amount of numbers between 1/3 and 1.
1/9 = 0.111...
0.111... x 9 = 0.999...
1/9 X 9 = 1
Hence, 0.999... = 1
No number inbetween. Identical numbers.
0.999...=1
It's a mathematical fact, and you've proved it with your final statement. What are you debating?