Introduction of *r of Super real number system

Entering the middle school math class, the teacher uniform a straight line on the blackboard. Question to the students: in this line, there are no two infinitely close to the point? Students immediately uproar, today's teacher is not "brain crazy"?

The teacher said to the students: modern quantum physics research shows that there is a shortest "line segment" (Planck length) in space. In a geometric line, if the distance of two points is less than the shortest segment, then these two points are called "Infinity". On the intuition, the students can easily accept this argument.

Then, the teacher said to the students: this geometric line is 1965 The "Super Straight Line" (also called "Super Real Number") introduced by American mathematician Robinson, does not lead to logical contradiction. Thus, the introduction of the definition ": the number (point) of infinity near the Origin o " is called "Infinity", and the inverse of the non-0 infinitesimal is called "Infinity".

when a moving point x Infinity close to a fixed point a x a

Middle School students learn a little new things, the sky will not collapse. The reality is that the geometric line can accommodate a variety of mathematical structures, far from only the standard real number R a numerical system. At present, American middle school students generally accept the concept of Super real *r .

Description: In the super-line, "infinite approach" is an equivalence relationship with transitivity. An infinitely close point forms a "list" (Monad), which is the concept of Leibniz. There is only one "standard real number" in the finite list, which is equivalent to the completeness of the real number system.

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Introduction of the *r of the Super real number system