.9 repeating = 1? Is our numerical system flawed?

Originally posted by nataylor
But you CAN'T stiuck a 9 "at the end" because there is no end on which to stick it. The nines go on forever.

This is where your reality stops, and mine begins. You see..

A circle has no begining and no end right? It is infinitly looped in a circle, creating a circumfrence. What if I wanted that circumfrence to be larger? How do I add on to something that is infinite? Do I add to the end? The beginning? The middle?

Believe it or not, you add to the end.

Infinity DOES have an end, it just takes infinity to get there.

You claim you can't add a 9 to the end, because there is no end.. You are wrong...

That is like saying you can't add "infinity + 1" but you can.

[edit on 2-4-2008 by ALLis0NE]

Originally posted by nataylor
Actually, that question proves my point. What you subtract from 1 to get .9... is 0. Because .9... and 1 are equal.

Actually that just proves that you and millions of other confused mathmeticians including wikipedia, are lost.

1 - 0.1... = ?

reply to post by ALLis0NE


Infinity + 1 = Infinity. By it's very definition, infinity means there is no end. If it had an end, it would be finite.

Originally posted by ALLis0NEActually that just proves that you and millions of other confused mathmeticians including wikipedia, are lost.

1 - 0.1... = ?

.1... = 1/9

1 - 1/9 = 8/9 = .8...

Originally posted by nataylor

Originally posted by ALLis0NEActually that just proves that you and millions of other confused mathmeticians including wikipedia, are lost.

1 - 0.1... = ?

.1... = 1/9

1 - 1/9 = 8/9 = .8...

You didn't answer the question.

What is 1 - 0.1...?

It is not .8... that is your rendition of it because of your mathmatical mistake of thinking 0.1... = 1/9

If something is infinite how can it equal 1/9?

1/9th of infinite?

Saying that 0.1... is equal to 1/9th is like sayin infinite DOES have an end. Which then would make it true that the number between 1 and 0.9... is 0.9...9

It's just infinite with an extra 9. At the end, in the middle, in the front, where ever you stick the 9, that is your answer.

0.9... will never equal 1




[edit on 2-4-2008 by ALLis0NE]

reply to post by ALLis0NE


You fail to grasp that a fraction can be represented by an infinitely repeating decimal. .1... does indeed equal 1/9. If it doesn't, what is 1/9 - .1...? You're placing limits on infinity that it doesn't have, by it's very definition.

You say put the extra 9 at the end, middle or front. An infinitely repeating decimal doesn't have an end, and it doesn't have a front. Therefore it has no middle since the middle is some fraction between the front and the end.

[edit on 2-4-2008 by nataylor]

This is very quite simple to understand ok?

Lets do it like this...

Get a calculator, clear it, then press the number 1.

From there, your goal is to get the calculator to say 0.9...

How do you do it? Subtract right?

reply to post by ALLis0NE


I don't know about you, but I certainly don't have a calculator capable of displaying an infinite number of digits. A calculator is incapable of displaying .9... or using it in a calculation.

Originally posted by nataylor
I don't know about you, but I certainly don't have a calculator capable of displaying an infinite number of digits. A calculator is incapable of displaying .9... or using it in a calculation.

So you admit to being wrong then.

If a calculator can't possibly use .9... in its calculation, then how do humans do it? You don't.

This is precisely the exact location of your error.

Try again.

It is common knowledge, common FACT, that to go from 1 to 0.9... you have to SUBTRACT. If you SUBTRACT that means you have LESS THAN 1.

0.9... < 1

0.9... != 1





[edit on 2-4-2008 by ALLis0NE]

reply to post by ALLis0NE


There are plenty of software applications like Mathcad, MatLab, etc. that are capable of dealing with infinitely repeating decimals. No hand-held calculator is.

What specific number for you subtract from 1 to get .9...?

[edit on 2-4-2008 by nataylor]

Originally posted by nataylor
What specific number for you subtract from 1 to get .9...?

It doesn't matter what the specific number is, it only matters that you have to SUBTRACT.

If I told you the sepcific number to subtract, you would say the number doesn't exist.

reply to post by ALLis0NE


If you have to subtract, there MUST be a specific number. And you're right, I would tell you such a number doesn't exist. It must be a decimal, then some number of zeros, and then a 1. But because we have an infinite number of 9s we need to reach, we'd need an infinite number of 0s. Every time to add a zero between the decimal and the "ending" 1, you make the number smaller. When you reach an infinite number of 0s between the decimal and the 1, you've made the number infinitely small. An infinitely small number is equal to 0.

Originally posted by nataylor
If you have to subtract, there MUST be a specific number. And you're right, I would tell you such a number doesn't exist. It must be a decimal, then some number of zeros, and then a 1. But because we have an infinite number of 9s we need to reach, we'd need an infinite number of 0s.

Exactly. The number is:

.0...1

But you don't believe that exists, but it does.

Originally posted by nataylor
Every time to add a zero between the decimal and the "ending" 1, you make the number smaller. When you reach an infinite number of 0s between the decimal and the 1, you've made the number infinitely small. An infinitely small number is equal to 0.

NO, zero is not a number. If you have an "infinitely small number" than that is what you have, A SMALL NUMBER.

small number != zero

reply to post by ALLis0NE


.0...1 is actually incorrect notation. Since the zeros go on forever, you'll never reach an end on which to put a 1, so that's why there is no number between .9... and 1. There is simply no room to fit a number between the two, making them equal.

Originally posted by nataylor
.0...1 is actually incorrect notation.

HUMANS INVENTED NOTATION.

There is no correct notation for this number. If it were to have notation, it would look like this...

.0...1

Originally posted by nataylor
Since the zeros go on forever, you'll never reach an end on which to put a 1, so that's why there is no number between .9... and 1. There is simply no room to fit a number between the two, making them equal.

This is where you are getting confused. You do not have to reach the end, before you put the 1 in it. Look at the notation...

.0...1

Imagine the ... is a never ending constant stream of 0's, and no matter what there is always a 1 at the end. Just imagine right now that something is adding 0's right in the middle where all the ... are forever "growing without bounds". Just add more and more and more zero's infinitly, and no matter what, you will always have the 1 on the end...

It's exactly like the circle anology I told you. Even though a circle has no beginning and no end, doesn't mean I can't add to it.

The number you are seeking is a never ending growing chain of zeros, and at the end of the infinite number of zeros is a 1.

Think of it like a prediciton of the future. Although you will never reach the end of infinite, if you ever do, there will be a 1 there..

It's simple logic..

What is 1 divided by infinity? Infinity.


THE FACT STILL STAND..

You have to SUBTRACT from 1 to get 0.9...

Do you agree or disagree that 1/3 can also be expressed as .3...?

Originally posted by ALLis0NE
What is 1 divided by infinity? Infinity.

Actually, 1/infinity is undefined. You can't divide 1 by infinity. Infinity can't be operated on.

[edit on 2-4-2008 by nataylor]

To ALLisONE

About that circle analogy. A circle is not infinite, only continuous. You can pick a point on a circle, go around the circle, and hit that same point again. Anything else is simply repetition. That's where your analogy falls apart. The more 9's you add to 0.9, not 0.999...., the more it defines it. However, you cannot count the 9's in 0.999..., since it is infinite, without limit or boundary. You can't add another nine on the end, just as much as you can't add a 1 on the end of 0.000..., because as far as you travel down the road of 0's, or 9's for the other example, the more there are, you will NEVER reach the end, as THERE IS NONE!!!

Now, about that whole "if a calculator can't do it, humans can't" business. Who do you think invented calculators? Take a long think...now guess. If you guessed anything other than humans, you are not smarter than a fifth grader. Humans invented the mathematical equations on which calculators operate. We are to calculators as Chuck Norris is to us: GOD!

A way to think about the first issue is a concept I came across in a college lecture: Hotel Infinity. In this scenario, a woman goes to a hotel seeking a room. However, in this hotel, there are an infinite amount of rooms, but all of them are full. Can the woman get a room? The answer is no, since all the rooms are full and YOU CAN"T CREATE ANY MORE ROOMS! THERE ARE ALREADY INFINITE ROOMS, a number you CANNOT surpass.

Also, you said "The number you are seeking is a never ending growing chain of zeros, and at the end of the infinite number of zeros is a 1." A number is static, it doesn't grow. And anyway, infinity can't grow, since for something to grow, it must first be defined, which infinity is not.

And finally, you said "You have to SUBTRACT from 1 to get 0.9... " NO, you DON'T, because they ARE EQUAL.

Oh, and stop giving us this "This is where your reality stops, and mine begins" crap. The only extra understanding of reality you have is that of a reality you created, or at least tried to create.

[edit on 4/2/08 by 00Einstein]

Originally posted by ALLis0NE
This is an easy one to understand, you must not think complex or you will get lost. The simple answer is the correct one.

.9 can NEVER = 1

Everything on the RIGHT SIDE OF THE DECIMAL, is only a PART.

A fraction, a part, a piece, a section of.

.9 is 9/10ths of 1

The more numbers you add after the decimal, makes it SMALLER. What people don't understand is you can ALWAYS DIVIDE.

No matter how small something is, you can always divide it into smaller. (hence infinite)

Case Closed

Sure fractions are only a part in reference to what is being measured, but in themselves they are their own whole and they can also be fractioned off.

In this respect .9 is its own one or its own whole. Because there is also a .9 of .9.

You must always think complex else you will be outdone by those that do.

In your post you completely contradicted yourself starting out by stating that .9 can NEVER equal 1, then later saying that things can infinitly be divided into smaller parts. Remember that a part is in itself its own whole, thus .9 is 9/10 of a specific 1, but in itself 9/10 is its own whole and there can be a 9/10 of that 9/10. So 9/10 does = 1 and so does every other number! And 1=0!

[edit on 2-4-2008 by LastOutfiniteVoiceEternal]

Originally posted by 00Einstein
To ALLisONE

About that circle analogy. A circle is not infinite, only continuous.

It is infinitely continuous as continuity implies infinity if there is no say of otherwise.

Infinity is immeasurable. A circle can be measured. A circle exists of the true nature of infinity but is not infinity itself. A circle is a limited line that is wrapped around to have its start and end conjoined and its "parts" amalgamed.

So as said above: your circle analogy fails. A circle is not an immeasurable singularity, only infinity is.