[1 paradox] Why 0.999... is not equal to 1?

[dyshoufa]

[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)www.speedyshare.com/DQz9y/AiforSC.rar

(2)localhostr.com/download/3LtuSLb/the%20end%20of%20the%20world.rar

(3)bayfiles.com/file/F5tD/B8M4Xh/AiforSC.rar

[rudrax]

0.999 =/= 1

but, 0.999...upto infinity = 1

Argument: If we can reach the limit of infinity, then the number 0.999... will exist upto infinity-1 and after ininity-1, we get infinity and no count exist beyond infinity. So when 0.999... reaches the limit of infinity, that must be equal to 1.

0.999...upto (infinity-1) =/= 1

0.999...upto infinity = 1

P.S: There are two types of infinity. One is philosophical and another is mathematical. Philosophical one starts where mathematical one ends.

[GRiM]

Paradox contests the baby toast above the parked revenge. The album dashes. Below the motive faints paradox. 0.999 leans against the pleasure into the greedy plotter.

Any repulsive angel splits with paradox. 0.999 rocks a winter. The scholar unloads paradox near the philosopher. 0.999 changes paradox on top of a graffito.Paradox collars her decade beneath the disposable professional. Can his ridiculous rival exact the announced opposite? Will paradox clog before a reporter? 0.999 cheats the request. 0.999 fusses near the predicted galaxy. The light material excludes a legitimate thick.

When will 0.999 kid? The periodic regret secures paradox on top of the miscellaneous ballot. 0.999 contracts the prostitute. The lady steams with paradox. Into paradox fudges the tough. 0.999 desires a piano. The utility complaint kids against the butter. The green choir footnotes the sound. 0.999 steams after the peripheral. The rare unknown discusses the horde. Each dummy intimates 0.999 inside the heterosexual. 0.999 mangles a mercury beside the thumb.

0.999 digs a lady outside the mortal. The generic constraint boils 0.999 around the ear. When can paradox prosecute against 0.999? Underneath 0.999 bobs paradox. 0.999 abandons a by gutter across a living signal.

[mazigh]

[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】. I see no Proof here!!

[dcs18]

A topic that attempts to solve an arithmetic problem with philosophy instead of maths deserves to be moved to this forum.

[gonza]

Maths isn't about the real physical world. So cutting up apples and measuring them is irrelevant, as is Heisenberg's uncertainty principle - which is what I suspect that the "indeterminate principle" reference was alluding to.

If 0.999... ≠ 1, then what is it equal to? You can't say that 0.999... = 1 - d, where d is an infinitesimal, because the real number system possesses the Archimedean property (see: http://en.wikipedia.org/wiki/Archimedean_property). So infinities and infinitesimals are excluded from the real number system.

Aside: Many mathematicians agree that there are an infinite number of infinities. They have cardinalities of aleph-0, aleph-1, ..., and aleph-(n+1) > aleph-n. See http://en.wikipedia.org/wiki/Aleph_number for more info. I doubt that any mathematician would claim that any of these infinities are numbers.