About 1 and 0.999999 ...... this problem in China Branch discuss it, oh, no, arguing, oh, no, a lot of fight, or, as the subject matter of a quarrel very common.
Today just saw this post, is that on this issue, "1 and 0.99999999 ...... controversy has very deep mathematical ideas" http://tieba.baidu.com/p/6177458659 ,
There are some thoughts on this issue.
The problem often is that "outstanding student" used against the people department, said people believe that families are not equal to 0.999999 ...... do not understand higher mathematics,
Oh, I do not bother you nobody knows for sure, you think 1 is equal to 0.999999 ...... just superstition official department only.
You ask Newton and Leibniz, equal to 0.999999 ...... 1, which do not, they will not have a clear answer,
There are 100 mathematicians, there are 100 possible answers.
Well, gossip does not say, I talk about my views,
1 is not equal to 0.999999 ...... It is obvious that this is clearly set up logically.
Why it seemed equal to 1 in the calculus 0.999999 ......? Why calculus is equal to 0.999999 ...... because you can get the theoretical values calculated by the model of continuous calculus.
Calculus seems ...... 1 equal to 0.999999, and because calculus is a dynamic situation, it is not static,
Static occasions, is not equal to 0.999999 ...... this is clear.
What is the dynamic of the situation?
You by 0.999999 ...... -> 1 to calculate the derivative, although not quite 0.999999 always to 1, but the location of this happening is the derivative of points, length and width to 0 is a singular point,
Therefore, the singularity and "Always 0.999999 to 1 not quite" both made a compensation equivalent to each other, so that you can use an equivalent substitution derivative calculation this point 0.999999 .......
Do not worry this is not accurate, if this point is the size (length and width), then with 1 equivalent substitution 0.999999 ...... really inaccurate,
But this point has no size, so with 1 equivalent substitution 0.999999 ...... it accurate.
Simply put, if the width is 0.0000000 ...... 1 point, then the derivative should be used to calculate ...... 0.999999,
However, if the width of the points is 0, the derivative can be calculated by 1,
It's that simple, OK?
I saw the post, said, "Until a certain period, a mathematician was proved equal to 0.999999 ......"
Also demonstrated what proof? I proved this article is much simpler than him.
Further, the number of (differential) is just a guide on the mathematical characterization, strictly speaking, can not reflect the real meaning,
Calculus practical significance is reflected in the final score,
By integrating the plurality of infinite differential piled up, which in itself is of a width at a point 0 1 of another compensation equivalent substitution 0.999999 ...... used.
Therefore, differential reflects the theoretical value on the abstract sense, reflects the integration of theory on practical significance.