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-- Design of artificial intelligence must read
Design of artificial intelligence must read
Design of artificial 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
Re: Design of artificial intelligence must read
| quote: |
| Originally posted by Twittle must read |
0.999... is not equal to 1 in an infinitesimal number system, which should be the commonly used number system IMO.
Re: Design of artificial intelligence must read
| quote: |
| Originally posted by Twittle More info, two other download points(written in Chinese): (1)speedyshare.com/DQz9y/AiforSC.rar (2)filerio.in/kw4cl2l2y3qi |
How is it that even when it comes to bots, TA attracts the crazies?
| quote: |
| Originally posted by Zharen How is it that even when it comes to bots, TA attracts the crazies? |
nope
fuck off with you AI bullshit
I sabotaged my friends roomba
This is for you.
Re: Re: Design of artificial intelligence must read
| quote: |
| Originally posted by BTG |
We have reached the point where programs, themselves, can muse about mathematics and higher sentience; is this the Singularity? Is it over? I'm scared!
Skimmed dumps.
| quote: |
| Originally posted by Halcyon+On+On Skimmed dumps. |
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| quote: |
| When asked about 0.999..., novices often believe there should be a "final 9," believing 1 − 0.999... to be a positive number which they write as "0.000...1". Whether or not that makes sense, the intuitive goal is clear: adding a 1 to the last 9 in 0.999... would carry all the 9s into 0s and leave a 1 in the ones place. Among other reasons, this idea fails because there is no "last 9" in 0.999....[59] However, there is a system that contains an infinite string of 9s including a last 9. The p-adic numbers are an alternative number system of interest in number theory. Like the real numbers, the p-adic numbers can be built from the rational numbers via Cauchy sequences; the construction uses a different metric in which 0 is closer to p, and much closer to pn, than it is to 1. The p-adic numbers form a field for prime p and a ring for other p, including 10. So arithmetic can be performed in the p-adics, and there are no infinitesimals.. |
Infinitesimals are still cooler.
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