The Instigator
jackgilbert
Pro (for)
The Contender
logicalcat181
Con (against)

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)
Comments (4)
Votes (0)

 

jackgilbert

Pro

For the first round please just accept the debate. Arguments will begin next round.
logicalcat181

Con

Hello, And thank you for posting this debate!
Debate Round No. 1
jackgilbert

Pro

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 re-write 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 1-0. 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
1-0. 999. . . . =0
This happens because 0. 99999. . . . =1. They are equal which is why when you subtract them you get 0.
logicalcat181

Con

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.
Debate Round No. 2
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Debate Round No. 3
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Debate Round No. 4
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Debate Round No. 5
4 comments have been posted on this debate. Showing 1 through 4 records.
Posted by felixmendelssohn 2 months ago
felixmendelssohn
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.
Posted by felixmendelssohn 2 months ago
felixmendelssohn
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.
Posted by uert 2 months ago
uert
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 non-mathematical equality?
Posted by felixmendelssohn 2 months ago
felixmendelssohn
facts are not to be debated.
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