The calculus reading room is not a math antique showroom

In July June 4, 2011, J. Keisler
Of infinitesimal calculus, which is written in chapter 1 of Chapter 1st: "... we
Build a hyperreal number system as an ultrapower (super power) of the real number system.
This proves that there exists a structure which satisfies the axioms ", meaning that there is a mathematical structure that satisfies the super real number of the system, and it is written to:" We
Conclude the chapter with the construction of kanovei and Shelah [ks 2004] of a hyperreal number system which is definable in set theory. this shows that the hyperreal number system exists in the same sense that the real number system exists. "What does this mean?

What is the "kanovei" of a super real number system?
And Shelah "build method? J. Keisler pointed out that this construction method is definable in the set theory ). Therefore, this leads to the conclusion:"
Hyperreal number system exists in the same sense that the real number system exists ", meaning that under this build method, the existence of the superreal number system is of the same significance as that of the real number system (
Same sense ). In mathematics, when is this scientific understanding strictly proved?

The actual situation is: in the symbolic logic magazine, the mathematician, James mirg, who worked in Moscow, Russia in 2004.
The cooperation between kanovei and S. Shelah proves this scientific conclusion. See the mathematical paper v. kanovei.
And S. Shelah, a definable nonstandard model of the reals, Journal of symbolic logic vol. 69 (2004), pages 159-164.

It can be seen that the establishment of the calculus reading room does not lag behind the trend of world development (2004. Its creation reflects the general trend of modern mathematics development. It has a profound theoretical background and is not an infinitely small "Antique" showroom. The central idea of this article is that the infinitely small calculus is an inevitable development stage (or trend) based on the contemporary theory of Public Physical and Chemical sets, and is not a private paradise of a few "alien.

Note: In 2011, J. Keisler wrote the "Foundation of Infinitely small calculus", which is a tutorial book specially designed for university mathematics instructors. The content is deeper, but it has more academic value. This book is the theoretical backing of the calculus reading room. It is not afraid of criticism, pick-up, and slander. With these three "not afraid", we are more confident.