Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**heibai****Member**- Registered: 2013-03-05
- Posts: 1

[1 paradox] Why 0.999... is not equal to 1?

Written in 2012

The current mathematic theory tells us, 1>0.9, 1>0.99, 1>0.999, ..., but at last it says 1=0.999..., a negation of itself (Proof 0.999... =1: 1/9=0.111..., 1/9x9=1, 0.111...x9=0.999..., so 1=0.999...). So it is totally a paradox, name it as 【1 paradox】. You see this is a mathematic problem at first, actually it is a philosophic problem. Then we can resolve it. Because math is a incomplete theory, only philosophy could be a complete one. The answer is that 0.999... is not equal to 1. Because of these reasons:

1. The infinite world and finite world.

We live in one world but made up of two parts: the infinite part and the finite part. But we develop our mathematic system based on the finite part, because we never entered into the infinite part. Your attention, God is in it.

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. That is to say, we can't use a number in the infinite world to plus a number in the finite world. For example, an apple plus an apple, we say it is 1+1=2, we get two apples, but if it is an apple plus a banana, we only can say we get two fruits. The key problem is we don't know what is 0.999..., we can get nothing. So we can't say 9+0.999...=9.999... or 10, etc.

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

2. lim0.999...=1, not 0.999...=1.

3.The indeterminate principle.

Because of the 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, or 0.11425, etc.

Now we end a biggest mathematical crisis. But most important is this standpoint tells us, our world is only a sample from a sample space. When you realized this, and that the current probability theory is wrong, when you find the Meta-sample-space, you would be able to create a real AI-system. It will indicate that there must be one God-system in the system, which is the controller. Look our world, there must be one God, as for us, only some robots. Maybe we are in a God's game, WHO KNOWS?

*Last edited by bobbym (2013-03-21 21:26:19)*

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

Hi;

1 / 3 is obviously .33333333...

2 / 3 is obviously .66666666...

Add them up:

---------------------------------------------

1 is obviously .99999999...

and that the current probability theory is wrong

The current probability theory is not wrong. The greatest empirical test of it was performed when Las Vegas was built pretty much by the efforts of Benjamin Siegel.

Every year the place proves probability works out here in the real world.

*Last edited by bobbym (2013-03-05 15:34:18)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

Why is it difficult for so many people to believe that 0.99999999999999....... = 1??

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

Beats me! I have heard every argument. None have ever been able to get through the first part of my post.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

You still haven't disproven me. It seems that including 0.999... in reals is arbitrary.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

Why would 1 being an element of the reals bother you?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Not 1. 0.999...

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

Do you agree that 1 / 3 = .3333333333... ?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Yes.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

You like the idea of 2 / 3 = .666666666...

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

That is okay, as well.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

.3 + .6 = .9

.33 + .66 = .99

.333 + .666 = .999

so

.3333333.... + .6666666 = .9999999

That is just notation so I hope you agree with that.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

I agree with the first three, but not with the fourth.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

It is just notation, ... means continuing on forever. This is obvious from the other ones.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

It is not. Strange things can happen at infinity.

You see, the point is not whether I believe 0.999... is 1 or not. I don't believe it exists in mathematics.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

Do you believe pi exists?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Yes. Otherwise, what would the ratio of the circumference and the diameter be?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

Do you have a problem with 3.14159...?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

No.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

So to you what does .999999... mean?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Something that is barred from maths.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

It is not barred from math. How would you write

.33333333... + .66666666... ?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

.33333333... + .66666666...=1.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

You do not see the possibility of

.3333333... + .6666666... = .9999999...?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

What is that 0.999... on the RHS. Doesn't look like a number!

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline