We are asked to find a function on such that that has positive derivative almost everywhere on that domain. It occurred to me to use the Cantor set, which is obtained by partitioning remaining intervals into thirds and removing the interior of the second one. So first then and , and so on. Each time we remove two-thirds of the remaining and summing the geometric series yields a measure of for all that is removed. Another Cantorian construct arrived at from the Cantor set is the Cantor function, or Cantor staircase, called such as it resembles a staircase. That is, it turns out exactly what we need. It is a function with derivative zero almost everywhere, with non zero derivative points as jump points at the Cantor set. It is that discontinuity that facilitates the going from to along an interval with zero derivative almost everywhere. A transformation of that with a function with positive derivative is a step to deliver us what we want. That would be minus the Cantor function. This has derivative almost everywhere. However, we need to keep its range inside , which its outputs at seems to not satisfy entirely. We are done though if we prove the other half to be non-negative, because then we can stretch the other half horizontally by a factor of two. It is needless to say that between and such is the case. Past , we have a downshift of in base three to a in base two at the first place, meaning a decrease of at least when summing the net change at all digits which decrease in value. Digits increase in value on a change from to in every place past the first, or on a digit in the original in its change to base two, which can occur only once, with all the following of that changed to zero, an increase of , where is the index of the place. In the former case, the largest possible increase is minus , which is . In the latter case, is exceeded by , the total decrease from digit to digit from the th place on. Thus, the minimum total increase from the increases exceeds the maximum total decrease from the decreases, which completes our proof of non-negativity for .
A result of Cantorian pathologies
Shenzhen based WeGene also gave very accurate height prediction. It's certainly possible that China had figured out this problem before Genomic…
点，你如果知道一个人的父母的姓氏，你就可以对他是北方人还是南方人有个有点统计显著 的估计。 读者可以在包含大姓分布图的…
包含其截屏链接： 祁晓亮的脸书政治言论 关于斯坦福反华反g及今年丑闻事件的知乎文章 在以上链接的知乎文章，有评论问为什么我认为祁晓亮是反华反g的。在这里我把他的脸书