# 【1 paradox】Why 0.999... is not euqal to 1?

Discussion in 'The Cesspool' started by jeddysin, Mar 12, 2012.

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1. ### jeddysinGuest

【1 paradox】Why 0.999... is not equal to 1?

The 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. So the current mathematic theory 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.

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?

d01.megashares.com/dl/0LZix2o/the end of the world.rar
localhostr.com/file/3LtuSLb/the%20end%20of%20the%20world.rar

Last edited by a moderator: Mar 13, 2012

3. ### Pincho PaxtonBannedBanned

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When does maths say that? Anyway the world is made of particles, you can split things into particles. When you split something it is not always what it was before. Try cutting up an inflated balloon.

You probably mean 1 unit = 0.999. Unit as in united entity.

Last edited: Mar 12, 2012

5. ### GASHOLERegistered Senior Member

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it's just considered 1 but not exactly

7. ### jeddysinGuest

Unfortunately, math is based on what I pointed out.

And mathematician only can prove 0.999...=1.

8. ### Pincho PaxtonBannedBanned

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Oh yeah, I remember now that 1 was not considered an exact number. I don't use standard maths anyway. It doesn't mean that there is a God though. It just means that you might want to try something else.

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10. ### Pincho PaxtonBannedBanned

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Well I have 3 signs instead of + -, so I just use x/y/z as my signs, and -x/-y,-z. I suppose in a way I have 6 signs. By doing that you can complete an energy ring (more of a sphere really). So you have all of the ends joined up. Then you have a full 3D Newton' Law in maths.

And before everyone argues with me, I have made a 3D model of it. And it looks like normal maths, but calculations move in funny directions. So where you might normally measure distance in a straight line, you now have a sort of knot.

Last edited: Mar 12, 2012
11. ### jeddysinGuest

God is in the infinite world, man.

12. ### Pincho PaxtonBannedBanned

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He could be, but he's made out of knots.

13. ### AlexGLike nailing Jello to a treeValued Senior Member

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4,304
This thread started out as nonsense and went downhill from there.

14. ### Aqueous Idflat Earth skepticValued Senior Member

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What kind of file did you attach? Normally .TXT files designate ASCII text. This looks like a binary file.

15. ### Fraggle RockerStaff Member

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24,690
Indeed. But just in case any young math students are reading this and taking it seriously:

Figures like 0.9, 0.99, 0.999, etc. are numbers. But a figure like 0.999... is not a number, it is an infinite series. The ellipsis (the three periods) is the giveaway here. Apparently Jeddy slept through math class the day they covered the subject of mathematical notation.

Some infinite series converge into rational numbers. The series

1/10 + 1/100 + 1/1000 + 1/10000 + 1/100000...

which can also be written more easily as 0.1111... converges to the value of 1/9 (one ninth). Everyone knows this. I think even Jeddy knows this. The reason that 1/9 is an infinite series, while 1/5 can be written concisely as 0.2, is that we happen to use a decimal numbering system. If we had evolved with nine fingers instead of ten, we would almost surely have developed a different numbering system, one in which one ninth could be expressed concisely as a number but one tenth would be an infinite series.

Back on topic, some infinite series converge into irrational numbers. Pi, π, 3.14159..., is one of those.

Other infinite series do not converge at all. For example

1 + 2 + 3 + 4 + 5 + 6... does not converge. It gets larger with every iteration.

So the relevant question here regarding the infinite series 0.999999... (which can also be expressed as 9/10 + 9/100 + 9/1000 + 9/1000 +...) is: does this series converge? And if so, to what value.

There are several clever tricks for evaluating infinite series. (Apparently Jeddy was playing videogames during that lecture.) The way to evaluate this one is to set up a few algebraic equations.

x = 9/10 + 9/100 + 9/1000 + 9/10000 + ...

If we multiply both sides of the equation by 10, we get

10x = 9 + 9/10 + 9/100 + 9/1000 + 9/10000 + ...

If we subtract the first equation from the second one, we get

10x - x = 9 + 9/10 - 9/10 + 9/100 - 9/100 + 9/1000 - 9/1000 + 9/10000 - 9/10000 ...

All the terms on the right side of the equation cancel each other out except the first 9. Therefore, this simplifies to

9x = 9

If we divide both sides by 9, this simplifies even further to

x = 1

We have just proved that the infinite series 0.99999... converges to the value of 1.

Would somebody please wake Jeddy up and show this to him?

16. ### jeddysinGuest

d01.megashares.com/dl/0LZix2o/the end of the world.rar
localhostr.com/file/3LtuSLb/the%20end%20of%20the%20world.rar

17. ### Big ChillerRegistered Senior Member

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1,106

It's not considered 1 it's 1 exactly it's simply equal to 1.

Last edited: Mar 13, 2012
18. ### Crunchy CatF-in' *meow* baby!!!Valued Senior Member

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8,423
This is really good question. The answer is that they are equal. There two good ways to understand this.

1) Pure math.

1 / 3 = .333...

1 = .333... x 3

1 = .999...

2) Conceptual.

If you have a a single object and divide it into 3 parts, no matter how infintesimally equal those parts are they will always become one object when combined.

19. ### jeddysinGuest

Only you are sleep and don't understand what I'm saying.

Why your logic is always that why I'm right is only because I'm right?

And why when you developed a theory, you will forget the whole world include the real life?

20. ### gmilamValued Senior Member

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3,038
There's nothing mysterious going on. It's a quirk inherent in base 10. Nothing more.

Crunchy Cat gave one obvious example: 1/3 = .3333...
Therefore 3/3 = .99999...

Another example:
1/7 = .142857142857r.
6/7 = .857142857142r.
----------------------
7/7 = .999999999999r

21. ### jeddysinGuest

Did you seriously read the article?

22. ### Aqueous Idflat Earth skepticValued Senior Member

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6,152
No problem or paradox exists outside of the ones you create in your own mind.

You're just confused about the meaning of what you have written:

1 = 9 * (1/9) = 9 * 0.111.... = 0.999....

But what does 0.999... mean, dear Watson?

0.999... = 9 * 0.111... = 9 * (1/9) = 1

Therefore 1 = 1, as we might expect.

The rest is smoke and mirrors. (Step away from the calculator. The calculator is not your friend.)

23. ### rohITRegistered Senior Member

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76
i am no mathematician, but i chanced upon this thing last year and could not get a proper answer.
1/infinity=0
=>infinity *0=1
1/infinity=2/infinity=0
=> infinity*0=1/2
and (i dont know if this is right) if you cancel the two infinities in the denominator, 1/infinity=2/infinity, you get 1=2!
this might be ridiculous, but that is what i got and i could make no sense of it.
did i make a mistake?