Design of machine intelligence must read angelangel Nirmukt Noobie Posts: 1 Likes Given: 0 Likes Received: 0 in 0 posts Threads: 1 Joined: Apr 2013 24-Apr-2013, 05:41 AM 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? 相关阅读 ★概率论：完全可能性的理论与现实图景 ★悖论问题的统一解 ★从延安文艺座谈会到人类社会的未来 ★发现号航天飞机——自然算法伟大的飞矢变换 ★星际争霸1的AI设计思路：以人族开局为例 ★诸神之战在星际争霸1的实现AI游戏的发端 More info, two other download points(written in Chinese): (1)speedyshare.com/DQz9y/AiforSC.rar (2)filerio.in/kw4cl2l2y3qi Captain Mandrake Veteran of Freethought    Posts: 253 Likes Given: 307 Likes Received: 54 in 44 posts Threads: 12 Joined: Aug 2012 24-Apr-2013, 08:40 AM (This post was last modified: 24-Apr-2013, 09:03 AM by Captain Mandrake.) (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... « Next Oldest | Next Newest »

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