The Instigator
Kaynex
Pro (for)
Winning
7 Points
The Contender
AtheistPerson
Con (against)
Losing
0 Points

The validity of 0.99999... = 1

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Post Voting Period
The voting period for this debate has ended.
after 2 votes the winner is...
Kaynex
Voting Style: Open Point System: 7 Point
Started: 12/5/2014 Category: Science
Updated: 2 years ago Status: Post Voting Period
Viewed: 1,045 times Debate No: 66412
Debate Rounds (5)
Comments (12)
Votes (2)

 

Kaynex

Pro

Well, here's a debate for fun. I am very much into math and this is how I roll.
Anyway, the debate is a common one seen over the internet, 0.999... = 1. That is infinite 9's. I am arguing that the statement is valid.

First round is acceptance.
AtheistPerson

Con

I am debating that .99... does not equal 1.
Debate Round No. 1
Kaynex

Pro

Thank you for accepting the debate AthiestPerson!

Before I begin, I'm going to let λ = 0.99999... so it is easier to read the work.

C1: They have no difference in value
Subtracting λ from 1 results in zero, showing they have no difference in value. They can be used similarily in an equation. Therefore, λ = 1

C2: You cannot make it "not 1"
λ to any power is still λ. This is a property that only the number 1 is capable of.
a*λ is infinitessimally less than a. This is also a property that only 1 is capable of.

C3: There is Mathematical proof of this
Let's begin by noting that λ can be made by just adding 9's infinitely.
In summation notation:
λ = Σ [9 / 10^n] --- {The sum goes from 1 to infinity}
λ = 9 Σ [1 / 10^n]
λ = 9 Σ [1 / 10]^n
This is just a geometric sequence, and can be solved using:
Σ a^i [from i=m to n] = [a^m - a^n] / [1 - a]
λ = 9[(1/10)^1 - (1/10)^infinity] / [1 - (1/10)]
λ = 9[1/10] / [9/10]
λ = 9[1/10][10/9]
λ = 1
AtheistPerson

Con

I have no clue how to use that symbol, so my representation will be
]{= .99999...

First, let me ask you a question; Do you think that .3333333 is equal to 1/3? What about .666666 being equal to 2/3?

Now I shall begin.

Here is my proof:

The function y=1-1/x is often used to show how the repeating decimal 0.9999... is equal to 1. When x=1, y=1; x=10, y=0.9; x=10000, y=.9999, and so on. The limit of 1-1/x as x approaches infinity equals 1. An assumption is often made, however, that if the limit of an expression as x approaches infinity is 1, then that expression must equal 1 when x equals infinity.

Assumption: 1-1/x = 1 when x = infinity
Subtraction: -1/x = 0
Multiplication: -1 = 0x
Zero Property: -1 = 0

-1 does not equal 0, therefore 1-1/x does not equal 1 when x = infinity.

You cannot treat "infinity" like a normal number, you can only think of it in terms of limits.

Some things to think about:

1. Saying ]{ = 1 is like saying 9999999999 = 10000000000. The numbers are completely different. They change completely.

2. Just because someone should not wish to write down the whole decimal out every time doesn't mean that it becomes the number one. At any time, you could make a simple symbol that represents the repeating decimal./
Debate Round No. 2
Kaynex

Pro

No problem that you can't use the symbol, the work was very easily read. For future reference though, you can copy-paste the symbol.

Just like division by 0, multiplication by infinity makes no sense and cannot be done.
For example, 3x5 = 3 + 3 + 3 + 3 + 3 = 15
But 3xinfinity = 3 + 3 + 3 + 3 + 3 + 3 +...
It doesn't come to a definite answer as an operation demands.

Essentially, this line:
"Subtraction: -1/x = 0
Multiplication: -1 = 0x"
Is flawed and cannot be done.

Rebuttal to 1.
λ = 1 is not like saying 9999999999 = 10000000000, because this would imply a finite amount of 9's.
Instead λ = 1 IS like saying 9999999999.99999... = 10000000000, and that is a statement that should be expected, since I implied that λa = a.

Statement 2 is a non-issue to the claim that λ = 1.
Debate Round No. 3
Kaynex

Pro

How much wood could a woodchuck chuck if a woodchuck could chuck wood?
AtheistPerson

Con

If a woodchuck could chuck wood, he would chuck a good amount of wood.
Debate Round No. 4
Kaynex

Pro

Would he chuck as much wood as he could?
AtheistPerson

Con

Yes, the woodchuck would chuck as much wood as the woodchuck could if the woodchuck could chuck wood.
Debate Round No. 5
12 comments have been posted on this debate. Showing 1 through 10 records.
Posted by MettaWorldPeace 2 years ago
MettaWorldPeace
I don't understand how you worded it, but your job isn't to enlighten me and I 'm not debating this, still maybe some people understand it, so your words aren't wasted.
Posted by Kaynex 2 years ago
Kaynex
It didn't like my unicodes... But lambda ^ inf = 1
Posted by Kaynex 2 years ago
Kaynex
Interesting question Metta, let's figure out.
Let _5;^W34; = L

By my definition of _5;:
L = lim[nU94;inf] (]1;[1U94;n] 9/10^n)^n
That summation is still 1, regardless if I put the ^n on it or not:
L = lim[nU94;inf] 1^n
L = 1
Posted by MettaWorldPeace 2 years ago
MettaWorldPeace
I have a question for Pro, what would lamda to the infinite power be set to?
Posted by Surrealism 2 years ago
Surrealism
Another reason that -1/x=0 does not follow to -1=0 is that zero times infinity is an indeterminate form. This meaning that it could equal any real number depending on the circumstances. In this case it equals -1.
Posted by Kaynex 2 years ago
Kaynex
Lol, it's NBD AtheistPerson, this debate is just for fun. Give it your best shot, there are ways to make it look invalid.
Posted by AtheistPerson 2 years ago
AtheistPerson
Sh*t. I'm not big on math so... anyways I just looked at it a different way. Boy am I f*cking r*tarded. I feel so stupid.
Posted by Kaynex 2 years ago
Kaynex
I agree, 0.999... does not ACTUALLY exist, and has no uses in the real world.

But this is math on paper. It has nothing to do with reality. Math is governed by a different set of rules, and I followed them to get to my answer.
Posted by Vajrasattva-LeRoy 2 years ago
Vajrasattva-LeRoy
More Gibberish ...

As L. Ron Hubbard stated in his 1950 book on Dianetics,
Absolutes have to be considered logically unobtainable.
Albert Einstein stated that the universe itself is finite but unbounded.
"Infinity" has no actual existence.
It's Impossible to get an infinite # of 9s.
Ergo, .999 ... cannot, & does not, = 1.
As a matter of fact, if you study Quantum Physics, 1 cannot exist.
Posted by SNP1 2 years ago
SNP1
Why are there people that still argue against truism on here? It is just another loss.
2 votes have been placed for this debate. Showing 1 through 2 records.
Vote Placed by lannan13 2 years ago
lannan13
KaynexAtheistPersonTied
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Total points awarded:40 
Reasons for voting decision: Concession
Vote Placed by carriead20 2 years ago
carriead20
KaynexAtheistPersonTied
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Total points awarded:30 
Reasons for voting decision: Con conceded.