# Thread: ★★★Proving 0.999... is not equal to 1★★★

1. Why 0.999... is not equal to 1? Because:

1. 0.999... is a number in the infinite world, but 1 is a number in the finite world.

For example, 1 represents an apple. But then 0.999...? We don't know. Because we live in a finite world, and then we develop our mathematic system.

We can use "infinite world" and "finite world" to resolve some of zeno's paradox, too.

2. Because of indeterminate principle.

Because of indeterminate principle, 1/9 is not equal to 0.111....

For example, cut an apple into nine equal parts, then every part of it is 1/9. But if you use different measure tools to measure the volume of every part, it is indeterminate. That is to say, you may find the volume could not exactly be 0.111..., but it would be 0.123, 0.1142, 0.11425, etc.

This standpoint tells us, our world is only a sample from a sample space. 2.

3. No it tells us that in practise we cannot measure a number to infinite accuracy. Not 0.33333333..., not pi, not 1.0, not 0. When you say a volume can be exactly 0.123, how do you know you have it exactly? Remember, at the end of every finite number is still an infinite number of zeros. However when a person says that 0.99999 = 1, they are speaking of the abstract objects known as the real numbers, which are constructed from a certain set of axioms and do not have to in any way accurately represent reality.

In real life we get only approximations, and in that way, 0.111111111... is as real as 1.000000000000...
But don't confuse math with real life, they do not have to agree, its just convenient that they often do. 4. Also, zenos paradox is a result of not knowing how to use arithmetic properly. 10x=9.999...
10x-x=9.0
9x=9
x=1 6. Originally Posted by TheObserver No it tells us that in practise we cannot measure a number to infinite accuracy. Not 0.33333333..., not pi, not 1.0, not 0. When you say a volume can be exactly 0.123, how do you know you have it exactly? Remember, at the end of every finite number is still an infinite number of zeros. However when a person says that 0.99999 = 1, they are speaking of the abstract objects known as the real numbers, which are constructed from a certain set of axioms and do not have to in any way accurately represent reality.

In real life we get only approximations, and in that way, 0.111111111... is as real as 1.000000000000...
But don't confuse math with real life, they do not have to agree, its just convenient that they often do.
No. It is your opinion but not mine gets mathematical theory, and then forgets the real life. Because you only use the theory.

And probability is the part of absolute truth, remember this. Certainly, it is not the probability theory you have learned. 7. Originally Posted by GiantEvil 10x=9.999...
10x-x=9.0
9x=9
x=1
An apple, plus one thing we even don't know what it is, is what?
Don't get into the theory and then only remember the theory. 8. Originally Posted by TheObserver Also, zenos paradox is a result of not knowing how to use arithmetic properly. 9. Math can be used to model reality but it isn't necessarily reflective of reality in any way. 10. Originally Posted by wikiday  Originally Posted by TheObserver Also, zenos paradox is a result of not knowing how to use arithmetic properly.
I can't read that, I'm sorry.

Zenos paradox was an old problem that resulted because the mathematical tools they had available at the time could not sum an infinite series. In modern decimal notation, the paradox doesn't even show up. 11. Originally Posted by TheObserver Math can be used to model reality but it isn't necessarily reflective of reality in any way.
You shall realized that the current mathematical theory is totally a paradox:

it says 1>0.9, 1>0.99, 1>0.999, ..., but at last it says 1=0.999..., a negation of itself. 12. Originally Posted by TheObserver  Originally Posted by wikiday  Originally Posted by TheObserver Also, zenos paradox is a result of not knowing how to use arithmetic properly.
I can't read that, I'm sorry.

Zenos paradox was an old problem that resulted because the mathematical tools they had available at the time could not sum an infinite series. In modern decimal notation, the paradox doesn't even show up.
Make a distinction between the infinite world and the finite world, you will resolve some of it.

There is no
relationship between math and zeno's paradox. 13. Originally Posted by wikiday 1. 0.999... is a number in the infinite world, but 1 is a number in the finite world.
You're confuscating integers with real numbers. These are two distinct sets. There isn't a 1 in the set of real numbers, but a 1.00000... with infinite zeroes. Likewise, 0.999... does not exist in the set of integers.

Likewise, your second example confuscates irrational with rational numbers. Irrational numbers are no less real that rational ones even though they cannot be expressed as a fraction of two integers.

it says 1>0.9, 1>0.99, 1>0.999, ..., but at last it says 1=0.999..., a negation of itself.
Only if the string of 9's are infinitesimally long. If they aren't, you are correct. 14. Originally Posted by wikiday but at last it says 1=0.999....
No it does not. It seems you understand very little of the subject. 15. Originally Posted by Wintermute  Originally Posted by wikiday 1. 0.999... is a number in the infinite world, but 1 is a number in the finite world.
You're confuscating integers with real numbers. These are two distinct sets. There isn't a 1 in the set of real numbers, but a 1.00000... with infinite zeroes. Likewise, 0.999... does not exist in the set of integers.

Likewise, your second example confuscates irrational with rational numbers. Irrational numbers are no less real that rational ones even though they cannot be expressed as a fraction of two integers.

it says 1>0.9, 1>0.99, 1>0.999, ..., but at last it says 1=0.999..., a negation of itself.
Only if the string of 9's are infinitesimally long. If they aren't, you are correct.
Your logic is, that why I'm right is because I'm right. 16. Originally Posted by Markus Hanke  Originally Posted by wikiday but at last it says 1=0.999....
No it does not. It seems you understand very little of the subject.
It is not I know little, but you have fell into a trap. 17. Originally Posted by wikiday Your logic is, that why I'm right is because I'm right.
And your problem is a complete lack of logic or mathematical understanding. Originally Posted by GiantEvil 10x=9.999...
10x-x=9.0
9x=9
x=1

Or this:
1/3 = 0.333...
3 x 0.333... = 0. 999...
3 x 1/3 = 1

Or this:
1 - 0.999... = 0.000...

Or the infinite number of other arguments that you are wrong ... 18. Warning: on another forum this "discussion" ran for 6 years years and 3,000 posts before the thread was closed for being too stupid.

A surprising number of otherwise smart people were on the wrong side. Although most of them changed their minds after reviewing the arguments.

I don't think anyone who started out with the right answer was persuaded that 1 != 0.999... (because that would be like persuading someone who can do arithmetic that 2+2 = 5). 19. Originally Posted by wikiday It is not I know little, but you have fell into a trap.
There are no traps; the maths is very clear.
0.9999... <> 1
Ref any elementary maths textbook.
This periodic number gets arbitrarily close to 1, but never reaches it. 20. Originally Posted by Strange  Originally Posted by wikiday Your logic is, that why I'm right is because I'm right.
And your problem is a complete lack of logic or mathematical understanding. Originally Posted by GiantEvil 10x=9.999...
10x-x=9.0
9x=9
x=1

Or this:
1/3 = 0.333...
3 x 0.333... = 0. 999...
3 x 1/3 = 1

Or this:
1 - 0.999... = 0.000...

Or the infinite number of other arguments that you are wrong ...
It seems that you don't know that "1+1=2" means, for example, an apple plus an apple, we get two apples, but not an apple plus a banana.

An apple plus a banana, we can say we get two fruit. But we don't know what 0.999... represent. That is to say, we couldn't use a number in the infinite world to plus a number in the finite world. It is the same to 1-0.999..., etc. 21. Originally Posted by Markus Hanke There are no traps; the maths is very clear.
0.9999... <> 1
Ref any elementary maths textbook.
This periodic number gets arbitrarily close to 1, but never reaches it.
Noooooo......  22. Originally Posted by wikiday It seems that you don't know that "1+1=2" means, for example, an apple plus an apple, we get two apples, but not an apple plus a banana.

An apple plus a banana, we can say we get two fruit. But we don't know what 0.999... represent. That is to say, we couldn't use a number in the infinite world to plus a number in the finite world. It is the same to 1-0.999..., etc.
I'm sorry, but we are talking about mathematics, which is a formalized system and doesn't feature any fruit. Simply making assertions and analogies is not a mathematical proof. 23. Originally Posted by Strange Warning: on another forum this "discussion" ran for 6 years years and 3,000 posts before the thread was closed for being too stupid.

A surprising number of otherwise smart people were on the wrong side. Although most of them changed their minds after reviewing the arguments.

I don't think anyone who started out with the right answer was persuaded that 1 != 0.999... (because that would be like persuading someone who can do arithmetic that 2+2 = 5).
Why they couldn't get the right answer is, this is a philosophic problem, not a mathematic problem. Math is a incomplete theory, and only philosophy could be a complete theory. 24. Originally Posted by Strange  Originally Posted by wikiday It seems that you don't know that "1+1=2" means, for example, an apple plus an apple, we get two apples, but not an apple plus a banana.

An apple plus a banana, we can say we get two fruit. But we don't know what 0.999... represent. That is to say, we couldn't use a number in the infinite world to plus a number in the finite world. It is the same to 1-0.999..., etc.
I'm sorry, but we are talking about mathematics, which is a formalized system and doesn't feature any fruit. Simply making assertions and analogies is not a mathematical proof.
You should know that this is a mathematical crisis. Resolve this, we may
enter a new era, a time of probability, philosophy, and even God. 25. Originally Posted by wikiday Why they couldn't get the right answer is, this is a philosophic problem, not a mathematic problem. Math is a incomplete theory, and only philosophy could be a complete theory.
So should we have this thread moved to philosophy where I can ignore it as meaningless speculation? 26. Originally Posted by wikiday You should know that this is a mathematical crisis.
I thought it was philosophy (and therefore of no practical value).

Resolve this, we
entered a new era, a time of probability,
philosophy, and even God.
Yeah, right. 27. Originally Posted by Strange  Originally Posted by wikiday Why they couldn't get the right answer is, this is a philosophic problem, not a mathematic problem. Math is a incomplete theory, and only philosophy could be a complete theory.
So should we have this thread moved to philosophy where I can ignore it as meaningless speculation?
No. Because when we get the two world, we will find God.

At first, you should know the current probability theory is a wrong theory. 28. When we get the right probability theory, we would be able to create a real AI-system, just like God. 29. Originally Posted by wikiday No. Because when we get the two world, we will find God.
Oh, good grief.

At first, you should know the current probability theory is a wrong theory.
And your proof for this is? Or is this just another random assertion? We can all do that: elephants are blue. See? 30. Because of Meta-Sample-Space.

Go to read #7 or this: forum4.aimoo.com/gg87667190

Maybe you should learn Chinese. 31. This is nonsense. Thread locked Bookmarks
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