Calculus is the grand entrance hall of the modern mathematics building.

Calculus is the grand entrance hall of the modern mathematics building.

As you know, you must first step into the lobby of the building. Kongji is the gatekeeper of the mathematics building. Anyone entering the math building must "Say hello" to the empty set ". The empty set contains no elements. Therefore, the empty set can also be expressed as {} (the mathematical symbol of the Set), and there are no elements in it.

In modern mathematics, digit 0 is generally defined as an empty set. Although the empty set {} is not a number 0. Therefore, number 1 is defined as {Ø}, number 2 is defined as {Ø, {Ø }},...... note: The inclusive relation of the set is "0", indicating the sequential relation of the natural number ,.......

Conway believes that all natural numbers still constitute a set of N. In this regard, the philosopher vigenstein resolutely opposed that set N has no mathematical significance. However, later people accepted the idea of Conway, accepted N is also a definite set, and thus the set N perfectly defines the rational number series Q.

Conway considers rational number sequence {rn}, n = 1, 2, 3 ,...... he believes that the rational number column {rn} of a "convergence" corresponds to a real number a. From then on, the real number system R is established. If we use the so-called "superfilter" to subdivide the sequence of the "kernel convergence", we will get the so-called "super real number" * R. This concept of "subdivision" of the number series was first proposed by Yuan Meng himself in the 1970s S.

There are two sets of real numbers, but we only have one set of calculus. In the modern mathematics building, any branch of mathematics cannot be separated from calculus ). Calculus "illiterate" is the modern mathematics illiterate!

Note: What is "cokeconvergence" and what is the "Filter" of the French burbaki school are technical details that do not impede the understanding of "Popular Science.

Yuan Meng, September