The Instigator
chilli0919
Pro (for)
Losing
0 Points
The Contender
lannan13
Con (against)
Winning
4 Points

Is 1/3 = 1

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Post Voting Period
The voting period for this debate has ended.
after 1 vote the winner is...
lannan13
Voting Style: Open Point System: 7 Point
Started: 4/24/2014 Category: Education
Updated: 3 years ago Status: Post Voting Period
Viewed: 812 times Debate No: 53256
Debate Rounds (3)
Comments (10)
Votes (1)

 

chilli0919

Pro

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.
lannan13

Con

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.
Debate Round No. 1
chilli0919

Pro

chilli0919 forfeited this round.
lannan13

Con

All points extended.
Debate Round No. 2
chilli0919

Pro

chilli0919 forfeited this round.
lannan13

Con

All points extended. Please vote Con.
Debate Round No. 3
10 comments have been posted on this debate. Showing 1 through 10 records.
Posted by PeacefulChaos 3 years ago
PeacefulChaos
Because while it is plausible to form an argument for the claim that 0.999 ... = 1 because there is no number "x" between the two, you can't use the same argument for the fact that 0.333 = 1, since there are numerous numbers "x" between the two.

E.g. 0.4, 0.45, 0.5, etc.
Posted by lannan13 3 years ago
lannan13
How are you confused.
Posted by PeacefulChaos 3 years ago
PeacefulChaos
Isn't that what I just said?
Posted by lannan13 3 years ago
lannan13
Pro is arguing that .333=1
Posted by PeacefulChaos 3 years ago
PeacefulChaos
I'm confused

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.
Posted by creedhunt 3 years ago
creedhunt
That isn't the topic of this debate though, do it's irrelevant
Posted by creedhunt 3 years ago
creedhunt
The difference is currently debated amongst mathematicians, but they are both potentially valid. It all depends on infinitesimal theories. https://www.google.ca...
Posted by The_Scapegoat_bleats 3 years ago
The_Scapegoat_bleats
Not true.
1/9 = 0.111...

0.111... x 9 = 0.999...

1/9 X 9 = 1

Hence, 0.999... = 1

No number inbetween. Identical numbers.
Posted by creedhunt 3 years ago
creedhunt
Actually, the number in between 0.999... and 1 is just infinitely small. That means there is no digit for it, as it is the opposite of an irrational. 0.000...1.
Posted by The_Scapegoat_bleats 3 years ago
The_Scapegoat_bleats
http://en.wikipedia.org......

0.999...=1
It's a mathematical fact, and you've proved it with your final statement. What are you debating?
1 votes has been placed for this debate.
Vote Placed by ESocialBookworm 3 years ago
ESocialBookworm
chilli0919lannan13Tied
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Total points awarded:04 
Reasons for voting decision: Obvious winner is lannan13. No questions asked. Conduct: FF, Args: his made more sense.