The Instigator
Pro (for)
1 Points
The Contender
Con (against)
3 Points

Without mathematical formulas, 0.999.... Does NOT Equal 1

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Voting Style: Open Point System: 7 Point
Started: 5/1/2014 Category: Miscellaneous
Updated: 7 years ago Status: Post Voting Period
Viewed: 15,265 times Debate No: 53653
Debate Rounds (4)
Comments (23)
Votes (1)




I believe without mathematical arguments, you cannot prove 0.9999.... equals one. In fact I will disprove this famous mathematical fact using arguments that aren't mathematical.
round one acceptance only
you can use any kind of argument (even troll!) but you cannot use any mathematical arguments
breakage of any rules results in full 7-point forfeit.

This debate is impossible to accept because I have school work to do. I will make this available in summer.


I accept this debate, and I intend to show that 0.9999.... does equal one.
Debate Round No. 1


Darn! This debate was supposed to be impossible to accept.
Ah well. I will type this as fast as I can.

1. The look completely different, thus, they aren't identical, and identical means equal, and because such, 0.999.... does not equal to one.
Seriously, look at them. They're completely different!

2. The Kalam Cosmological Argument
The KCA says this:
"The basic argument[edit]
  1. Whatever begins to exist, has a cause of its existence (i.e. something has caused it to start existing).
  2. The universe began to exist. i.e., the temporal regress of events is finite.
  3. Therefore, the universe has a cause.

Following Al-Ghāzāli, Craig argues that this cause must be a personal will.[5]

The first sub-set of arguments[edit]

Argument based on the impossibility of an actual infinite:

  1. An actual infinite cannot exist.
  2. An infinite temporal regress of events is an actual infinite.
  3. Therefore, an infinite temporal regress of events cannot exist.
The second sub-set of arguments[edit]

Argument based on the impossibility of the formation of an actual infinite by successive addition:

  1. A collection formed by successive addition cannot be an actual infinite.
  2. The temporal series of past events is a collection formed by successive addition.
  3. Therefore, the temporal series of past events cannot be actually infinite."
Because of this, 0.999... cannot actually go on forever. Thus, there is a llimited amount of 9's, and the limited amount of 9's can never make it so close to one that 0.000....1 equals to zero.

3. Because I'm happy
Pharrell William's "Happy" song's lyrics state "I'm a hot air balloon, I could go to space". However, had he been a 0.999.... hot air balloon, there is no way he could make it to space, and he wouldn't be happy, contradicting his lyrics and making a horrible song.

Onto you, con!
(And remember, no mathematical arguments!)


For your first argument, you claim:

"The[y] look completely different, thus, they aren't identical, and identical means equal, and because such, 0.999.... does not equal to one. Seriously, look at them. They're completely different!"

But appearances are not enough to state that two things are not the same. This is a dog:

click="document.location='/GaryBacon/photos/album/3762/24391/'" src="../../../photos/albums/1/4/3762/3161-3762-cmqps-a.jpg" alt="" />

But this is also a dog:

click="document.location='/GaryBacon/photos/album/3762/24390/'" src="../../../photos/albums/1/4/3762/3161-3762-mmpfr-a.jpg" alt="" />

The two look completely different, yet both are considered dogs. A difference in appearance is not sufficient to claim that two things are different.

The Kalam Cosmological Argument

First, I must commend you on your creativity. Using an ontological argument for this debate is certainly thinking outside the box. Nevertheless, this argument which was designed to show the existence of a God has been viewed as invalid by many in the philosophical community.

The argument itself argues against infinites, and then establishes God as necessary for the existence of the universe. Yet, by definition, God is an infinite. This argument refutes itself.

But since this debate is not of an ontological nature, there are further points to the argument that must be addressed.

The argument against infinites

Craig's main argument here uses an analogy of a library with an infinite amount of books. However, this analogy cannot be applied to all infinites. The following two links show the problems with the Kalam Cosmological Argument.

In addition to showing the problems with the Kalam Cosmological Argument, we can actually see that contrary to Craig's views, infinites do exist. The universe itself is, in fact, an infinite and the universe does exist.

Lyrics to Pharrell Williams' "Happy"

The lyrics to the song may state "I'm a hot air balloon, I could go to space" but this doesn't mean that these lyrics are true. First off, I think that it is fairly obvious that Pharrell Williams is NOT a hot air balloon.

Furthermore, even if he were a talking, singing, hot air balloon, he would not be able to go to space because a hot air balloon cannot rise fast enough to exceed the escape velocity needed.

So while I agree that a 0.999.... hot air balloon would never make it to space (which is simply another way of saying a hot air balloon), it is because I am familiar with physics and not because I believe there is any difference between a hot air balloon and a 0.999.... hot air balloon.

My argument

Now that the rebuttals have been handled, I will show why 0.999.... and 1 are, in fact, the same.

When two things are different, we are always able to show what the difference is between the two. Two things are said to be the same when there is no difference between the two. When looking for a difference between 0.999.... and 1, there is no difference.

Because infinites do exist, 0.999... can go on forever, and so anyone that tries to show me the difference would show me 0.000... going on forever. Therefore 0.999.... and 1 are the same since there is no difference between the two. And when two things cannot be shown to have any difference, the conclusion is that they are equal.
Debate Round No. 2


*claps hands* Well played, well played!
1. The dogs which look the same
They're both dogs, but not the same kind of dogs!
0.999... and 1 are both numbers, but not the same kind of numbers.
Thus the argument is refuted.

2. The KCA
Your sources try to prove that actual infinites are completely possible. It is true that the creator of the argument couldn't prove an infinite doesn't exist. On the other hand, I am a genius, and I can prove the KCA. So, it would take forever to write down "0.999.....". You'd get closer and closer every time you write a "9", but you never reach the full 0.999.... that equates to one. This infinite cannot possibly exist because you cannot write down all the "9"'s, or even have a computer display all the "9"'s, and you will never reach the number that equals to one.

3. The Hot Air Balloon cannot make it to space
You are wrong, my friend. Pharrell is so happy he creates a magical rainbow that boosts him up into space. See the picture below if you don't believe my claims.

See? This teeny tiny rainbow can support a unicorn plus leprechaun nearly 15 times its size. Obviously full rainbows can support much, much more, and Pharrel the Hot Air Balloon can defy the laws of physics, making it to space.

Now, I still have tons and tons of characters left, so here I will introduce a new argument and hope it is sufficient to disprove 0.999.... equals one.

4. Rage Man

So, how is this relevant to my argument? Well, you see, let me code the numbers below and you will see.
F=0, U=9. Let us assume there is a random period in between a "F" and an "U" in the above picture.
Since 00000000000000000=0, the above post states a man yelling "0.9999....".
Now, what is one? Well, it can't possibly be F, or U. And since the coding seems random, I will assign it a random value: E. "E", although is the most commonly used letter in the English language, does not appear in "FFFFFFFFFFFFUUUUUUUUUUUUUUUU-". Thus, one cannot equal to 0.9999.....
If one does equal to 0.999...., which is impossible, then we are assigning a number, not a letter, but an incomplete word. If we assign every letter a different letter, one cannot possibly equal to "FFFFFFUUUUU", since that is WAY over one letter.
What if we assign the letter "F" or "U", you may ask? Okay, first let us assume "1" is assigned "F". So now, the guy raging could be shouting "0.9999..." or shouting "1111111111.99999...". Obviously this is not equal. Now, let us assume "1" is assigned "U". So now, the guy is either shouting "0.99999...." or "0.111111....". These are not equal either.
Thus I have refuted my opponent's arguments and proved that 0.999.... does not equal to 1.


1. Things that look different are not necessarily unequal

To show that two things can look different and yet be equal, I chose to use dogs in order to minimize any use of numbers to avoid any accusations of a mathematical argument. However, I acknowledge your point that they are two separate breeds of dog, and therefore not completely equal.

Therefore, I will use another analogy to show that two things CAN be equal while looking completely different. This is obvious to anyone that has any familiarity with Roman numerals. Roman numerals are represented by letters of the Phoenician alphabet, and look completely different from the Arabic numerals that we use today. If one were to write any number larger than one in Roman numerals and then in Arabic numerals, the result will be two completely equal numbers that look different from one another. I believe this example shows that the argument of 0.999.... and 1 looking different shows nothing, as we can find many equal values that look different and yet remain equal.


No person can ever write out 0.999.... and no computer can ever display this number. On this point, I wholeheartedly agree with you. However, I disagree with your conclusion. The fact that no person, machine, or anything else could ever possibly fully write out 0.999... does not mean that infinites do not exist. In fact, the very point you make actually shows that infinites do exist. If a person, machine, or anything else were ever able to write out all of 0.999... then, no matter how large it is, it would be finite by definition. The fact that this feat cannot be accomplished shows that infinites do exist.

In addition, I have used a real life example to show the existence of infinites. The universe is infinite! No person, machine, or anything else could ever possibly explore ALL of the universe. It is impossible. But just because this feat is impossible, it does not mean that the universe does not exist. It is obvious that the universe does exist. The universe is also an infinite. Therefore, infinites DO exist.

Pharell's Hot Air Balloon

Regardless of the song lyrics or rainbows, the hot air balloon does not make it to space. Pharell is most likely on LSD if he thinks a magical rainbow will support his weight (a rainbow is a simple dispersion phenomenon and not a tangible object). But even if his hot air balloon did make it into space, a 0.999.... hot air balloon in such a case would also make it to space. They are one and the same. The song lyrics do nothing to refute the equality of 1 and 0.999...

The Rage Man

In this example, the man is shouting "FFFFFFFFFFFFUUUUUUUUUUUUUUUU-". From here, you assign values to the letters (and place a decimal point between the final F and the first U). But the argument that was created from this holds no water. The fact that he is not shouting "1" in this example, but "0.999...." does not show that the two values are unequal.

In fact, it seems that you have merely taken your very first argument (i.e. they look different therefore they are different) and converted it from a visual standpoint to an auditory one. In essence, the Rage Man example simply claims that since the two sound different they are not equal. But this argument contains the same flaw as the visual example.

If an American screams out "Eighty eight!" and a Japanese man screams out "Hachi ju hachi!" the two sounds produced will be completely different. Yet the value of what is screamed by each remains the same. So the fact that this man screaming "0.999...." in code is not screaming "1" instead does not show that the two are unequal. Just as two values can look different yet remain equal, two values can also sound different and remain equal.

The remaining arguments of 1111111.9999999.... and 00000.9999999.... not being equal is obvious. These are not the values we were debating as equal (nor is 000.1111...) and so this section I will justifiably ignore.

My argument

To reiterate, any two things that are unequal must be different in some way. Yet when looking at the difference between 0.999... and 1, we have no difference in value. As pointed out by you, we do have differences in visual appearance and in the way they sound when spoken (or shouted). But the difference in value, if one were asked to show it, is simply 0.00000....

If there is no difference shown between these two numbers, they are of equal value. Therefore, 0.999.... does, in fact, equal 1.

Debate Round No. 3


This debate has been pretty fun, I have got to say!
Now, onto the final rebuttals and conclusion!
The Roman numerals at least look something alike the numbers they represent. The difference between infinite characters and one character is impossible to calculate, while the difference between 4 and IIII are only three characters, far from infinity.

Keep in mind that the universe was either created by God or some other formidable force with omnipotent powers are near omnipotent powers. However, since 0.999... Was created by us mere humans, and our power is nowhere near the power needed to create something a grand as the universe, there is no possible way for us to create an infinite number.

Well, for one, "I'm a zero point nine nine nine repeating balloon" would have too many syllables, ruining the song. Furthermore, fans could misinterpret these lyrics as " a balloon repeating the words "zero point nine nine nine" for eternity. This new number, 0.999, does not even come close to one. Argument refuted.

The languages may mean the same thing, but they are still different words nevertheless.

I have disproved 0.999... Equals one. Vote pro.



Equal vs. Different

To show that two values may be equal, but look different, I gave the example of Roman Numerals. I believe that this is sufficient to show that two different looking symbols can represent the same value.

Nevertheless, I will address your point. Your claim is that Roman numerals and Arabic Numerals have some similarities, and that my argument would crumble if we were to introduce infinite characters. But this is clearly not the case. There are MANY values that can be represented in a short form but also in a repeating decimal. This does not mean that because one is shown right away (e.g. circumference of a circle/diameter of a circle) and the other is a decimal that goes on to infinity that the two values are not equal. The voters can verify for themselves that there are many fractions which go on to infinity when converted into decimals. The fact that the decimal form stretches on forever does not negate the fact that it is EQUAL to the fraction form.

0.999.... is simply a repeating decimal form of 1. The fact that one goes to infinity does not mean that they are not equal.

Infinite Existing

Your claim is that the universe was created by some omnipotent force, while 0.999... was created by humans. This is completely false. Numbers have existed long before humans ever existed. Humans did not invent numbers. We discovered them. The only thing humans invented were the symbols that we use to represent the numbers. But the numbers have always existed and are a part of nature.

Secondly, this argument started out as your attempt to disprove the existence of anything infinite. It seems that with my last argument, you have now conceded on the point that infinites do exist.

Pharell Williams

This argument is a rehash of the previous argument. Basically, you are claiming that since the number one can be spoken (or sung) right away and that a repeating decimal would make a terrible (impossible) song lyric, that the two values are not equal.

But I have just explained how repeating decimals can be fully equal to something else that is represented in another format that one can write or speak or sing. Of course "I'm a 0.999.... hot air balloon" would not be a suitable lyric. I wouldn't dream of arguing that point. But this does not show that 1 and 0.999.... are not equal.

The fact that repeating decimals can't be used as titles or song lyrics means nothing. Take the following movie for example:

The movie title would be impossible to represent as a repeating decimal. But the repeating decimal version is still equal to the movie title.

Rage Man

I will merely reiterate this point, since it does not appear to have been addressed.

The Rage Man example is the auditory version of the argument that things that look different cannot be equal. I have already shown that two things that look different can still have equal values. It follows that when these two different sounding but equal values are shouted, the different sounds produced do not negate the equality of the two values. See my previous argument for the example.

My own argument (repeated now for a third time, and still never addressed)

If two values are not equal, then there must be some difference between the two. Since the difference between 1 and 0.999... is 0.000... then the two must be equal. No difference between two values means that those two values are equal.

To 9spaceking:

I really enjoyed this debate. Your arguments were very original and creative. Good luck.

Debate Round No. 4
23 comments have been posted on this debate. Showing 1 through 10 records.
Posted by 9spaceking 7 years ago
no one voting? Aw man...
Posted by Buggie111 7 years ago
In my book, a mathematical argument is an argument that includes mathematical concepts, which those certainly are.
Posted by 9spaceking 7 years ago
they are mathematical concepts, we just said them in weird ways. (infinity concerning objects and the universe, and set variables as a "code")
Posted by Buggie111 7 years ago
Fine then. Addition. Infinity. Variables (F=1, U=9). All three of those are mathematical concepts
Posted by GaryBacon 7 years ago

I see your point, but if the mere mention of numbers counted as presenting a mathematical formula, then both 9spaceking and myself have violated the rules.

The mere mentioning of numbers is inevitable. The debate was based on trying to prove the equality of the two values without using the various mathematical formulae and proofs to show that the two are equal. Numbers were mentioned, but no equations or formulae were used. I think we both kept in line with the rules.
Posted by Buggie111 7 years ago
They include mathematical concepts, which is enough for me.
Posted by 9spaceking 7 years ago
Well, those aren't mathematical theorems or mathematical arguments.
Posted by Buggie111 7 years ago
You mentioned both numbers ( a mathematical concept) and addition (also a mathematical concept). IMO, that's forfeit worthy.
Posted by 9spaceking 7 years ago
I didn't disprove the theorem using mathematical concepts, tho, so I don't lose any points. :3
my arguments shortened:
--the 2 numbers look nothing alike
--some scientific theory
--lyrics from a song
Posted by Buggie111 7 years ago
And 9spaceking with a 7 point forfeit.

"Among mathematical objects are numbers"

Discussing mathematical concept=forfeit
1 votes has been placed for this debate.
Vote Placed by Anonymous 7 years ago
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Total points awarded:13 
Reasons for voting decision: Conduct to Pro for creativity? And arguments to Con because Pro's were bizarre and Pro never addressed the difference between 0.9r and 1.

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