A mathematical discovery that will spread around the world and be written into all university textbooks

A mathematical discovery that will spread around the world and be written into all university textbooks

Self-selected "beyond the Turing Machine" SeriesArticle:
Beyond the Turing Machine (II)-mysterious and infinite
Http://blog.csdn.net/universee
(2) answers to the mysteries of mathematics in the past century

In the conto set theory, it is considered that there are no number of infinity. conto obtains a series of infinity, ∞ 0, ∞ 1, ∞ 2… with "The set power set base is greater than the set base ...... ∞ N ......
∞ 0 is the number of all natural numbers (Natural Numbers = rational numbers = non-exceeded numbers ......)
∞ 1 is the number of all real numbers (number of real numbers = points in a straight line = points in a line segment = points in space ......)
What is ∞ 2? Later, it was hard to think of "the number of all curves in space (which can be an n-dimensional space)", that is, the number of all possible mathematical functions (including continuous and discontinuous functions ).

∞ 3 and later one hundred have not found the actual meaning for many years and become the mystery of century mathematics.

Now I will solve this problem,
I will give the answer to this question and then prove:
∞ 3 is the number of all functions with functions as variables,
∞ 4 is the number of all functions whose values are "functions as variables,
∞ 5 is the number of all functions whose values are "functions with functions as variables,
......
This recursion goes on. In general, we can say:
∞ 3 is the number of all functions,
∞ 4 is all generic functions,
∞ 5 is the number of all generic functions,
......
∞ N is all generic ...... Number of functionics (a total of N-2 extensions ),
......
This Recursion

In fact, we need to have a profound understanding of the concept of the set's idempotence to solve this problem. From the set theory, we have learned that the Set's idempotence is a set composed of all the subsets of the set. What is an equivalent concept? I said: "The set composed of all subsets" is actually all the relationships between elements in the original set! See.

This is enough,
For example, ∞ 3 is the number of relationships between all elements of ∞ 2 (all mathematical functions). That is not the number of all functions whose functions are variable)? Understand Why ∞ 3 is the number of all functional functions.

∞ 4 is the number of relationships between all elements of ∞ 3.
∞ 5 is the number of relationships between all elements of ∞ 4.
......
Recursion

By the way, there is a simple,
∞ 2 is the number of relationships between all elements of ∞ 1 => ∞ 2 is the number of relationships between all real numbers (all possible relationships) => isn't that the number of all possible mathematical functions? (Including continuous functions and discontinuous functions, which can be n functions );
∞ 1 is the number of relationships between all elements of ∞ 0 => ∞ 1 is a real number (note that a real number can be mapped to an n-dimensional space ).

In the future, we will also discuss the consortium set theory and several non-consortium set theories.