Is Cantor continuum assumed to be correct?

as you know, in 1874 , Cantor used the "diagonal method" to prove the real-number set (also called "Continuum"), Continum ) is an irreducible collection that makes mathematicians eye-opener. However, the real number itself is not the smallest irreducible collection, when Cantor himself did not know. In order to figure out the problem, Cantor did his best, but it was fruitless.

The continuum is not the smallest irreducible set, which is a fundamental problem for the basic research of mathematics. For this reason,1900 , at the Second World Congress of Mathematicians in Paris, France, was listed as the first unresolved issue (a total of all the questions) and brought to the attention of the world's mathematicians.

in the last century - years, on the basis of the axiomatic set theory, the great mathematician (Goder) with Cohen ( Cohen ) proves that this problem is beyond the scope of axiomatic set theory and cannot determine its authenticity.

By this century, theThe American-born "Little Head"William Hugh Woodin(1955-in this paper, it is pointed out that there is a "real class" between the real set and the set of numbers (Proper class) instead of the collection (Set). In this sense, the set of real numbers is the smallest infinite set of irreducible numbers is a "true proposition".

Thus, Cantor's hypothesis about continuum (that is, there is no infinite set of irreducible numbers smaller than real numbers) is a genius guess, close to mathematical truths. The reality is , this problem is still the forefront of the basic research of mathematics.

Description: Recently, a "little Hair" (female) after reading Post, to express their own views. I personally hope that all of you will come and discuss the issue.

Shimen 6 Month - Day

Is Cantor continuum assumed to be correct?