does 0. 9999999. . . . . . . . . . Equal 1
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Voting Style:  Open  Point System:  7 Point  
Started:  8/12/2018  Category:  Philosophy  
Updated:  2 months ago  Status:  Debating Period  
Viewed:  356 times  Debate No:  117669 
Debate Rounds (5)
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For the first round please just accept the debate. Arguments will begin next round.
Hello, And thank you for posting this debate! 

There are a few proofs I would like to present that 0. 999. . . . . Equals 1.
Algebraic proof 1: Let's give 0. 99999. . . A name, It may or may not be one but for this argument let's give it the quantity name X x=0. 9999. . . . Let's multiply both sides by 10 10x=9. 999. . . . . So far so good Let us rewrite 9. 9999. . . . As 9+ 0. 9999. . . . 10x=9+ 0. 9999. . . . We know from the top that 0. 99999. . . . . =x so we can substitute 10x=9+x Subtract x from both sides 9x=9 divide both sides by 9 x=1 If we replace the x at the very top with 1 because we now know that x=1 we get 1=0. 9999. . . . . Algebraic argument 2: 1/3=0. 3333. . . . . Multiply both sides by 3 3/3=0. 999999. . . . . . . 3/3=1 so we substitute 1=0. 99999. . . . . . . Argument 3: If 0. 99999. . . Does not equal 1, We should find a number between them. If not, If they are equal, Then 10. 9999. . . . Should equal 0, Let's subtract 0. 99999. . . . . From 1. 1. 000. . . 0. 9999. . . . . . ========== 0. 00000. . . . . There is no end to the 0's. 0. 0000000. . . . =0 10. 999. . . . =0 This happens because 0. 99999. . . . =1. They are equal which is why when you subtract them you get 0.
0. 9999999 does not equal one as I have already said one difference. There is still a 0. 0000001 difference between the two. X cannot equal one. (Your first equation was wrong as the answer would be negative. 

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4 comments have been posted on this debate. Showing 1 through 4 records.
Posted by felixmendelssohn 2 months ago
when someone debate a mathematical fact, You assume they play the same rule, Inferring from the same axioms. Its unreasonable to have to list every assumptions and definititon before entering a debate.
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Posted by felixmendelssohn 2 months ago
sure, But since the instigator did not redefined an alternative def of equal, I assume he meant it in the traditional sense. Plus, Your definition of equality based on appearance is silly because the point of the equal sign is to equate expressions that appear to be different.
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Posted by uert 2 months ago
Theoretically, There is a whole world of philosophical middle ground to debating this question including several deeper investigations of mathematics. In addition, Providing a different definition of "equals", There is a whole new debate that could be had. It's undisputed for instance to say that they don't at least look different. Is that enough to prove distinction in terms of nonmathematical equality?
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Posted by felixmendelssohn 2 months ago
facts are not to be debated.
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