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[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?

More info, three other download points(written in Chinese):
(1)speedyshare.com/DQz9y/AiforSC.rar
(2)localhostr.com/download/3LtuSLb/the%20end%20of%20the%20world.rar
(3)bayfiles.com/file/F5tD/B8M4Xh/AiforSC.rar
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[1 paradox]   Why 0.999... is not equal to 1?

But it is, so you don't need to bring God into it.

http://en.wikipedia.org/wiki/0.999...

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The equality 0.999... = 1 has long been accepted by mathematicians and is part of general mathematical education.
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but 1 is a number in the finite world.
1 is also a number in the infinite world.

Mathematicians say finite world == N and the infinite == R   
N is a subset of R so all finite numbers are infinite too.
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Quote
but 1 is a number in the finite world.
1 is also a number in the infinite world.

Mathematicians say finite world == N and the infinite == R   
N is a subset of R so all finite numbers are infinite too.


I was told there would be no math in this class?  smiley-wink

Lefty
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I like philosophy

take a circle with diameter 1.   (finite)
It circumference is 3.14159265..... aka PI (infinite)

Dependant of how I describe the circle -  by its diameter or circumference - it is finite or infinite.
So the circle is both at the same time.

The Shrek theory:
An union is 1 like the apple is 1.
I can peel of one layer so making the onion smaller than 1 (its like dividing the apple)
but it is still an onion.
So the onion is at the same time 1 and smaller than 1. (finite and infinite)

In physics this is called dualism(?)  like light is a particle (finite) and a wave (infinite)

Think you should also read - http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
which states in short "you cannot proof anything unless you start with assumptions...."
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http://en.wikipedia.org/wiki/Principia_Mathematica

In the book Principia Mathematica by Alfred North Whitehead and Bertrand Russell they took about 360 pages to prove 1 + 1 = 2, a proof that was later discredited by Kurt Gödel.

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"From this proposition it will follow, when arithmetical addition has been defined, that 1+1=2." —Volume I, 1st edition, page 379 (page 362 in 2nd edition; page 360 in abridged version). (The proof is actually completed in Volume II, 1st edition, page 86, accompanied by the comment, "The above proposition is occasionally useful.")
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1 + 1 = 2 is an Axiom and therefore true by definition (and then only in an non curved space (Euclidian) Math IIRC)

BTW as programmers we all know that 1 + 1 = 10 smiley-wink
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