The Instigator
Pro (for)
2 Points
The Contender
Con (against)
0 Points

.999... is equivalent to 1

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Post Voting Period
The voting period for this debate has ended.
after 1 vote the winner is...
Voting Style: Open Point System: 7 Point
Started: 10/27/2015 Category: Science
Updated: 2 years ago Status: Post Voting Period
Viewed: 542 times Debate No: 81610
Debate Rounds (4)
Comments (5)
Votes (1)




My position: The mathematical value of .999... is equivalent to the value of 1.


1. No semantics, kritiks, or trolling.


R1: Acceptance. Con can ask to clarify terms, but cannot make new arguments.
R2-3: Rebuttals.
R4: Closing remarks. No new arguments in R4.


anything you can pick up with your hand is 1
Debate Round No. 1


Hello, vi_spex. Thanks for accepting! However, let's remember that Round 1 is fo acceptance, so I'm not going to address the argument made there until a bit later.

I'm just going to jump in, demonsrating a few proofs that the mathematical value of .999... is equivalent to the mathematical value of 1.

A Proof by Geometric Series

This proof is actually utililzed in the link that someone posted in the comments.

First, we expand .999... as .9 + .09 + .009 + ...

We notice that an equivalent way to show this expansion is:

9/10 + 9/100 + 9/1000 + ....

which is:

9/10 + 9/10 * (1/10) + 9/10 * (1/10)^2 + ....

This is now clearly recognizable as a geometric series, with the first term a = 9/10 and the common ration, r = 1/10. Since the absolute value of r is less than one, we can use a special formula to calculate the sum of the entire infinite series:

Sum = a * [ 1 / (1-r) ]

Plugging in, we see:

.999... = (9/10) * [ 1 / (9/10) ] = (9/10) * (10/9) = 1

A More Common Proof

This proof is perhaps one of the most utilized proofs in demonstrating that .999... is equivalent to 1.

Let x = .999...

We can multiply each side by 10, which effectively moves the decimal place in .999...:

10x = 9.999...

Now we can subtract 1x from both sides:

10x - x = 9.999... - .999... =
9x = 9

By simply dividing both sides by nine, we see that:
9/9x = 9/9 =
x = 1

There are quite a few more proofs on this issue, but I will reserve those for later, based upon what my opponent has to offer. I'd like to remind my opponent that this is a mathematical issue, so he would be wise to approach it in a way that is mathematically sound and utterly devoid of metaphors.


what are you expanding, how do you expand a stone?

destruction is impossible in reality, rock is rock
Debate Round No. 2


Oh boy.

To start, the opponent did not attempt to refute my arguments and merely addresses one of them with an ill-formed metaphor.

To answer my opponents question, "what are you expanding, how do you expand a stone?":

I am expanding a mathematical expression. I did not claim to expand a stone, nor do I wish to learn how to expand a stone.

As for his claims about destruction, those aren't relevent here.

Vi_Spex, I specifically said there was to be no trolling. Please use the next round to produce more serious arguments.


i can expand on a unicorn by making it grow or changing it into a black unicorn with a golden horn, but i cant pick it up from the floor
Debate Round No. 3


I don't think troll debates are fundementally bad. They can often produce some great comedy. However, I made it clear in Round 1 that trolling was a direct violation of the rules. I should be awarded the full 7 points for this debate because of this rule violation.

However, in the off scenario that my opponent isn't trolling and that he is simply being...him... I will address what he has said.

My opponent has claimed he has the ability to expand a unicorn, by which he means change it. However, he has not sufficiently proven the existence of unicorns, thus leading us to believe that vi_spex cannot change what does not exist.

Additionally, he stated that he could not pick the unicorn up from the floor. This is entirely opinionated, as the opponent has likely never seen a unicorn. For all he knows, if a unicorn exists, it may be very light. In fact, the unicorn might only be slightly heavier than air; so light that even a mouse could pick it up off the floor. There is no way of knowing without adequate proof.

Also, the opponent's comment is irrelevant to the debate.

I have demonstrated that .999... is equivalent to 1. These arguments were not contended.

I have also heard that winning a debate against vi_spex actually lowers your ELO. I imagine that this is poetic justice, as I mentioned in the comments that I created this debate because I thought it would be an easy win. I didn't even consider the fact that a win could actually hurt my rankings. If that was your intent in debating me vi, well done. Point made. I'll have to create a minimum ELO for acceptance with my next debates.

Vote Pro.


unicorns are imaginary.. you understood what i wrote, thus a black unicorn with a golden horn must exist

so pick up 0.999 stone
Debate Round No. 4
5 comments have been posted on this debate. Showing 1 through 5 records.
Posted by vi_spex 2 years ago
your lack of comprehension is on you, you just pick up 0 sodas from the floor

Posted by AllenFierte 2 years ago
I'm sorry that you are up against vi_spex. He's a troll and/or idiot. (This was the result that was reached after a debate between him and another person on whether or not vi_spex was a troll.)
Posted by Sarai.K82 2 years ago
Interesting debate, I read the explanation and still only vaguely understand the concept.
Posted by Cobalt 2 years ago
I am so trying to gain ELO right now. This topic seems like one that people would argue against.
Posted by HipsterCloud 2 years ago
I agree, I have trolled so many math teachers with this.
1 votes has been placed for this debate.
Vote Placed by logical-master123 2 years ago
Agreed with before the debate:-Vote Checkmark-0 points
Agreed with after the debate:-Vote Checkmark-0 points
Who had better conduct:Vote Checkmark--1 point
Had better spelling and grammar:Vote Checkmark--1 point
Made more convincing arguments:--Vote Checkmark3 points
Used the most reliable sources:--Vote Checkmark2 points
Total points awarded:20 
Reasons for voting decision: Okay first of all Con trolled. He had bad spelling too. 2 points to go to Pro.