测度、数轴的概念与几何基础问题

Points with only position but no size are called ideal points, which have the property that can not be pointed out. In practical applications, it is necessary to use approximate points which can be drawn to represent the location of ideal points and have realistic properties. The length of line segment possess uncertainty to measure, and the ideal length is the limit of approximate length sequence whose error bound tends to zero. The argument on the axiom of parallel lines needs to be solved by materialist dialectics, and needs to be put forward concept of parallel lines which have relations of interdependent of approximation with ideal. Pythagorean theorem is a formal logic theorem under ideal geometric elements. The absolute quasi decimal expression of irrational radical number 2 does not exist. It is necessary to approximate its size with enough decimal digits. There is a relationship of interdependence and struggle between theory and practice. Geometric theory needs to be improved in practice, but correct geometric analysis theory can be used to modify the drawing of inaccurate geometric figures.)