What is in One: Uncertainty Quantum and Continuum Hypothesis

The concept of measurement is discussed. It is argued that counting process in mathematics is also measurement which requires a basic unit. The idea of scale is put forward. The basic unit itself, which are composed of the infinitesimal of uncertainty quantum, can be regarded as infinite in another scale. Thus infinite, infinitesimal and integer ”1” are unified. It is proposed that multiplication changes to summation when it is transformed to a larger scale. The Continuum Hypothesis is proved to be correct after a scale transformation. In the history of physics and mathematics, it is often seen that progress in one area depends on the progress in the other area, and difficulty in this area connects subtly with the difficulty in that area. From the perspective of physics, infinite in physics is a source of uncertainty and instability which has been haunting for a long time. Though many mathematical techniques have been developed in theory to deal with it, no further understanding of the concept has been got since it was first introduced. This is mainly because there has not been a breakthrough in the understanding of measurement in physics. Though this may sound a little bit strange, it can be seen when we think about the mathematical genesis of infinite. When Cantor introduced the family of infinite, he got it by continuous counting of integers. Obviously the counting is a measuring process with ” 1 ” to be the basic unit. Thus if we hope to get deeper understanding about the concept of infinite, we must have an inspection to the concept of measurement in physics. As is well known, the concept of measurement in quantum physics has been one of the most controversial point in modern physics[1]. We believe that progress for this problem relies on an overall and integrated understanding of The author is thankful for Prof. Lin Xie for beneficial discussion.