The Instigator
burnbird14
Con (against)
Losing
22 Points
The Contender
Sorrow
Pro (for)
Winning
25 Points

.999 Repeating is Equal to 1

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Post Voting Period
The voting period for this debate has ended.
after 11 votes the winner is...
Sorrow
Voting Style: Open Point System: 7 Point
Started: 3/25/2010 Category: Miscellaneous
Updated: 7 years ago Status: Post Voting Period
Viewed: 5,854 times Debate No: 11551
Debate Rounds (2)
Comments (45)
Votes (11)

 

burnbird14

Con

I hope my opponent accepts my debate, and I will thank him if he decides to do so.
I couldn't help but notice when I saw this debate posted, and I noted that his original opponent forfeited. I will not be so inclined.

Essentially, the term equals is defined by the Merriam Webster Dictionary as "to be equal to; especially : to be identical in value to." Unfortunately for my opponent, .999 is only an approximation of 1. Approximation is defined by the same source as "something that is approximate; especially : a mathematical quantity that is close in value to but not the same as a desired quantity." Further, my opponent's original argument that 1/3 equals .333... is flawed, because that is not true. It is only an approximation.
Consider this. By multiplying 1/3 by 3, you get 3/3, which, when divided, becomes 1. However, when you divide .333(continues on forever) by 3, you get .999 (continues on forever) which rounds to one. Therefore, not all fractions are direct representations of their decimal counterparts. Sometimes, they are approximate. This is one of those instances.
Sorrow

Pro

I accept your challenge. Thank you.

You have to understand the proper concepts of this before you take a stance on it. 1/3 equals to 0.3333 repeating, meaning it is infinite after that. It is not an approximation, it is INFINITY and repeating. Also, my original argument was simply that 0.99999999 REPEATING equals to 1. Approximations were never implied, as this is INFINITY we are dealing with.

Also, I am not too clear on your math, as when you divide 0.333 (I assume this to be repeating, so it's 1/3) by 3, you get 0.11111111 repeating. Dividing 3 by 0.33333 repeating equals to 0.99999.

And even if my logic is somehow flawed, there are many more scenarios which outnumber your premise. For all sake of arithmetic, 99.9999999999999% and repeating (no pun intended) of all mathematicians and scientists in the world will tell you that 0.9999999... = 1.

Is this scenario approximate?
.9_=x
10x=9.9_
minus x from both sides and you receive:
9x=9
x=1

Also, you cannot subtract from infinity. If you subtract 0.9999 repeating from 1.0, assume that the 0.1 will still be infinite, meaning your answer cannot be provided if it is to result in anything tangible. I hope this makes sense.

Thank you.
Debate Round No. 1
burnbird14

Con

I thank my opponent for accepting my challenge. I only wish we had more time to discuss this enthralling, but fallacied, theory.

To begin, I will state that the reason that a calculator gives 1/3 to be 0.3333....repeating on and on forever is that it cannot conceive the possibility of there being a fraction of a decimal, because it violates the code of mathematical conduct. However, this is the truth of the matter, because if 1/3 is 0.333... and 1/3, then, in turn, multiplying that by 3 will give us 1. Precisely 1, as it is supposed to be.

This theory is supported by various physicists, as well as my physics teacher, Mr. Smith, and the physics head of Royse City High School, Mrs. Powers. So, there you have it, since they must use calculus, the most complex of all mathematics branches, in physics calculations. Also, that disproves the theory that 99.999(on and on) percent of mathematicians and scientists agree with him on this subject. That argument is ENTIRELY false, because if 99.99999999% of math and science scholars agree with my opponent, then that leaves out at least two individuals of that category. Do the math, multiply 6 billion by .9999999999, see what you get.

Furthermore, my opponent's argument that .333 goes on forever is flawed, because it is a calculator value, not the true value. Again, 1/3 is actually 0.333 and one third.

I do apologize for my grammatical error when I said that by dividing .333 you get .999. That is untrue. I meant multiply, not divide.

Next, just because approximations are not implied does not mean that they don't have to be accounted for. Calculators must, in actuality, approximate the value of 1/3, because of the polite mathematical rule I mentioned before.

Continuing with my opponent's proof equation "scenario", it is not proper, because while it is true, I would again say that that does not conclude that .9999999999(forever and ever) equals 1/3. It doesn't prove it.

My opponent's closing statement also leaves us with no tangible proof, instead leaving us to ponder just how massive infinity truly is. Instead, my statement that 1/3 equals .333 and one third simplifies the issue, leaving the con side of this debate as the victor.

Thank you for this debate, it was very fun.
Sorrow

Pro

If a calculator cannot contrive the possibility of there being what you have stated, then how can humans possibly do so ourselves if we were the original inventors of the calculator? What separates a calculator's "mathematical conduct" and a human's "mathematical conduct"?

The only way for CON to win this argument is through a sophist's use of semantics. This mathematical conduct you speak of, would you please care to elaborate? Multiplying 1/3 by 3 would guarantee you precisely 1, as you have mentioned, but only because the fraction is IMPLIED as a whole number. If we were to take it piece-by-piece, which would be 0.33_, times that by three, then it cannot possibly equal 1, by logic. HOWEVER, the resulting 0.000_1 value is so small, it would have no use in mathematical equations. That's like saying subtracting infinity from infinity, or multiplying infinity by infinity, to reinforce my previous argument.

I do not see any theory here, just simple logistics. While indeed physicists employ calculus, what makes your physics professor have more merit than the word of a thousand other physics professors? Being a student myself, I know that there are at least a dozen ways of simplifying this equation in order for it to equal 1. I would not choose to go through that many variables, because it is time-consuming, but if you look at Wikipedia (oh God not Wikipedia!) then you'll find a plethora of premises which should satisfy you.

While I'm on this rant, I wouldn't so far as to say that calculus is the most complex of all mathematical branches, as that is subjective to the beholder. A 6 year old could say addition and subtraction is the most complex thing they've ever seen. Also, I was exaggerating my claims with a hyperbolic expression, you took it far too seriously. BUT, while we're on the subject of statistics, my proofs of 0.999_ equaling 1 totals up to much more proofs than you can claim on paper.

Practically, the statement is true. While it may not make sense from a logical point of view, in reality, that's all that matters.

"Furthermore, my opponent's argument that .333 goes on forever is flawed, because it is a calculator value, not the true value. Again, 1/3 is actually 0.333 and one third."

I don't see what you are trying to say here. Calculators can't input infinity, because it has no value. Therefore, CON saying that 1/3 is "actually 0.333 and one third" is false, because:

1. 1/3 is actually 0.333_ and so on...
2. You can't add a decimal ending in infinity to another ending in infinity

"Continuing with my opponent's proof equation "scenario", it is not proper, because while it is true, I would again say that that does not conclude that .9999999999(forever and ever) equals 1/3. It doesn't prove it."

If that equation cannot sustain your needs, then your words cannot sustain the given scenario. Words are not the same as numbers, either CON can start providing more mathematical proofs AGAINST 0.999_ = 1, or I am the victor.

As I've mentioned earlier, semantics is the only way for CON to win, albeit I think I have established enough high ground, so please vote for me, PRO.

Thank you.
Debate Round No. 2
45 comments have been posted on this debate. Showing 1 through 10 records.
Posted by Torrente 7 years ago
Torrente
infinity is a concept, not a number =o)D yea baby!!
Posted by Sorrow 7 years ago
Sorrow
Mathematical properties are not physical, you can't see 0.0000000 (ad infinitum) and 1 when applied to anything, that is not impossible either in real life or in math.

My logic is not flawed.
Posted by burnbird14 7 years ago
burnbird14
Even the fraction of a fraction of a fraction of a grain of salt has weight. Maybe not very practical or measurable, but weight nonetheless. Your logic is flawed.
Posted by Sorrow 7 years ago
Sorrow
1 exists as a whole number and a real integer.

0.000 (ad infinitum) ending in a single one, equals 0.
Posted by burnbird14 7 years ago
burnbird14
If .999 repeating is equal to one, then .000...1 must be equal to zero, because when you add them in the real world, they come out to one. However, We know that it cannot equal zero because that 1 exists, making it NOT zero.

What.
Posted by Sorrow 7 years ago
Sorrow
Which, of course, means that all of your arguments are inherently flawed and invalid as they all prove that 0.999_ equals to 1.

I win.
Posted by Sorrow 7 years ago
Sorrow
So if you didn't do anything wrong on paper, yet you essentially modeled the same equation I did, yet you said I could not have subtracted the two values, then your equation must also be meaningless, which begs the question of how it's meaningless mathematically.

The only thing that I can think of of being mathematically meaningless is the real number between 0.999_ and 1, which of course does not exist within any given superset.
Posted by nickthengineer 7 years ago
nickthengineer
No.

10x=9.999999

and

x=0.999999

are the same equation. You can't subtract the two. It's meaningless. But on paper, it makes all those repeating 9's go away which is why you like it so much. But it's still meaningless mathematically. Same as this:

x + y = 0
*multiply by 2
2x + 2y = 0
*therefore
x + y = 2x + 2y = 2(x + y)
*therefore
1=2

I didn't do anything wrong on paper but it's mathematically meaningless nonetheless.
Posted by Sorrow 7 years ago
Sorrow
Since this is an equation, we can multiply both sides by 10 and we have
10x=9.9...

We are allowed to subtract the same thing from both sides of an equations.
Since x=.9...
we subtract x from the left side and .9... from the right side. We can do this because they are the same thing. That is how we defined x, in fact. Now we have

10x-x=9.9...-(.9...)
which tells us

x=1

This is because the 1-x-9x=1x and the 9.9...-(.9...)=1
Posted by burnbird14 7 years ago
burnbird14
No need to be rude.
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