Does .999 repeating equal 1?

Thanks for accepting the debate.

I'd like to first start off with my definitions. According to the Free Dictionary, Repeating decimal is defined as a decimal in which a pattern of one or more digits is repeated indefinitely, for example 0.3535353535... Dictionary.com also defines repeating decimals as decimal numerals that, after a certain point, consist of a group of one or more digits repeated ad infinitum, as 2.33333 ". or 23.0218181818 ".

This means .999 repeating is endless. In other words, there are infinite amount of 9s in .999 repeating.

Here is a simple proof of why .999 repeating is equal to 1.

1/3= .333 repeating
2/3= .666 repeating
3/3= .999 repeating
3/3 also equals 1.
Thus, 1=3/3.
(1/3+2/3=3/3=1 is equivalent to .333...+.666...=.999...=1)

2nd Proof:

1. x=.999...

2. 10x=9.999...

3. 10x-x=9.999...-.999...

4. 9x=9

5. x=1

6. 1=.99999999...

(http://en.wikipedia.org......)

Refutations:

P1.1+1=2
P2.0.999+0.999= 1.998
C1.1X00;0.999

Judge, I'd like to point out that this argument is invalid.
.999 REPEATING does NOT equal to .999.
The topic clearly states: Does .999 REPEATING equal 1?
Thus 0.999+0.999 is completely different from 0.999...+0.999...

For all these reasons, please vote for the affirmative side of this debate. Thank you.

Sources:
1.) Khan Academy-
https://www.khanacademy.org...
2.) Purple Math-
http://www.purplemath.com...
3.) Calculator-
http://www.calcul.com......
4.) Dictionary.com-
http://dictionary.reference.com...
5.) The Free Dictionary-
http://www.thefreedictionary.com...

Thanks for the response.

Clarification:

1.) "Second, if first round was acceptance, then why did my opponent bring up an argument for me to refute?"

I am sorry. It was quite ambiguous. I meant to say that it was Con's objective to prove how .999 does not equal to 1. :)

Refutation:

1.) "So, then increasing 0.6666...(2/3) by 1/3 will equal 0.9999... never 1. Same applies backwards taking 1/3 away from 3/3 (0.9999...) will equal 0.6666... (2/3)"

Like I said, 0.999... is equivalent to 1.

.333... (1/3) plus .666... (2/3) equals .999... (3/3). 3/3 is equivalent to 1. Thus .999... must be equal to 1.

I'd like to remind my opponent that .999...=1. He never proved how they were different. Instead, he merely stated."1/3 will equal 0.9999... never 1."

Thus, my argument still stands.

2.) "If 3/3 = 1 then subtracting 1/3 (0.3333...) will not equal 2/3 (0.6666...) which it should"

If you put 1-1/3 in the calculator, you get 2/3 (.666...). In order to prove me wrong, you must explain why the calculator is wrong.

3.) "If 0.9999... was equal to 1 then 2 would be equal to 0.1818.... 3 would be 0.2727... 4 would be 0.3636...

A number cannot equal a number with a lesser value. That destroys the meaning of them being equal."

First of all, your argument doesn't make any sense. 2 is clearly larger than .1818... I don't understand where you got these numbers from. Your pattern makes no sense at all.

Second, we are only talking about the number 1.

My second argument was dropped. Thus, it remains standing.

I assume that he was unable to finish his previous speech. So, I urge him to continue.

For all these reasons, please vote for the affirmative side of this debate. Thank you.