Design of machine intelligence must read
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Design of machine intelligence must read

[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?

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More info, two other download points(written in Chinese):
(1)speedyshare.com/DQz9y/AiforSC.rar
(2)filerio.in/kw4cl2l2y3qi
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#2
(24-Apr-2013, 05:41 AM)angelangel Wrote: 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

Let us first take a look at the the part in red.

The ", ...," in "1>0.9, 1>0.99, 1>0.999, ...," is used to mean that 1>"Zero point 9 repeated for any finite number of times".

Let us next move to the blue part. The "..." in "1=0.999..." means "9 repeated an infinite number of times."

The part in green pretty much proves that 0.999... =1, where "0.999..." refers to "Zero point 9 repeated for infinite number of times" and "0.111..." refers to "Zero point 1 repeated for infinite number of times".

There is no paradox.

The problem is you failed to understand what "..." meant in the red part of your post and what "..." meant in the blue part of your post.

PS: Other proofs of 0.999... = 1 can be found here http://en.wikipedia.org/wiki/0.999...
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