The Instigator
SeventhProfessor
Pro (for)
Winning
5 Points
The Contender
Zoo903
Con (against)
Losing
0 Points

Does .999... Equal 1?

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Post Voting Period
The voting period for this debate has ended.
after 2 votes the winner is...
SeventhProfessor
Voting Style: Open Point System: 7 Point
Started: 11/5/2013 Category: Miscellaneous
Updated: 3 years ago Status: Post Voting Period
Viewed: 384 times Debate No: 40023
Debate Rounds (5)
Comments (2)
Votes (2)

 

SeventhProfessor

Pro

This will be a formal debate, following the following format:
Round 1; Acceptance
Round 2; Opening arguments and rebuttal for contender.
Rounds 3-5; Rebuttals, counterexamples, etc.

Definitions
= means absolutely equal to, not rounded in any way.
.9r means .9 repeating.

You must actually prove your point using either previously proven and/or universally accepted mathematical principals. All numbers are considered base 10 unless specified otherwise. Please don't use any math that I know for a fact you don't understand, as there could quite easily be flaws neither of us see. The fact that .9r=1 is already universally accepted among the mathematical community shall be ignored for the debate.
Zoo903

Con

We know that 1 is a rational number, that is, it can be expressed as a/b. Now if 0.999... is equal to 1, it too must be a rational number. This means that there exists c/d such that c/d = 0.999... However, no such c and d exist. So 0.999... is not a rational number. Therefore 0.999... cannot be equal to 1.also for the proof Let the decimal number in question, 0.9999", be called c. Then 10c W22; c = 9. This is the same as 9c = 9. Dividing both sides by 9 completes the proof: c = 1. It is stating that c is a variable and you should be able to replace the variable with any number and get the same answer on both sides of the equation but you don't.
Debate Round No. 1
SeventhProfessor

Pro

My opponent and I have met in real life. I explained the rules and we have agreed that his first argument will be disregarded, please don't let it count for or against either of us. I shall present three proofs.

First, the algebraic proof we both have most likely seen multiple times before, but written in a slightly different way:

.9r=.9r
*10
10(.9r)=9.9r
-.9r
9(.9r)=9
/9
.9r=1

Second, an irrational number proof, using pi as an example:

4.00000...-3.14159...=.85840...

As there is no last digit of pi, no digit of 4-pi will be large enough to "bump up" 3.14159...+.85840... to 4. Therefore,
(4-pi)+pi=3.9. I present the following proof.

(4-pi)+pi=3.9r
Associative property
4+(-pi+pi)=3.9r
pi-pi=0
4=3.9r
-3
1=.9r

My last proof is the simplest. 1/3=.3r, now multiply both sides by three. 1=.9r is the answer.

I conclude my opening statement and look forward to my opponent's.
Zoo903

Con

Zoo903 forfeited this round.
Debate Round No. 2
SeventhProfessor

Pro

FF, vote pro!
Zoo903

Con

Zoo903 forfeited this round.
Debate Round No. 3
SeventhProfessor

Pro

I extend my arguments.
Zoo903

Con

Zoo903 forfeited this round.
Debate Round No. 4
SeventhProfessor

Pro

I'm loving all of my opponents forfeiting...

Vote Pro!
Zoo903

Con

Zoo903 forfeited this round.
Debate Round No. 5
2 comments have been posted on this debate. Showing 1 through 2 records.
Posted by SeventhProfessor 3 years ago
SeventhProfessor
I know, it's just that this guy has been arguing this with me for a while.
Posted by Nilly 3 years ago
Nilly
How can you debate a mathematical truth?

It's like debating if 2+2=4, how can anyone be con that??
2 votes have been placed for this debate. Showing 1 through 2 records.
Vote Placed by Ragnar 3 years ago
Ragnar
SeventhProfessorZoo903Tied
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Total points awarded:10 
Reasons for voting decision: I don't see the problem with con's R1 arguments, but their dropping out means they cannot win arguments. Conduct goes to pro who stuck around... As for the issue, I hate early rounding (got into an argument with my econ teacher who rounded to the second decimal place on a test, and expected us to get the same answers without telling us...), but with the infinite it's at least damned close. Not sure if I'd use the equal sign instead of the approximation sign, but good arguments.
Vote Placed by imabench 3 years ago
imabench
SeventhProfessorZoo903Tied
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Total points awarded:40 
Reasons for voting decision: FF