News Sina china netease yahoo china chinese Peopledaily 文汇报 sciencetimes Pravda[R]

  University tsinghua peking zhejiang NanKai Nothease China Fudan Tongji Dongnan Teaching Dalian Doctor

  Goverment Edu SCI Internet China

  Mathematics manofmath liangpeiji maths faculty

There exist serious logical wrongs in the basic mathematical theory

Xin-dong. Ma

This segment consists of ten theses. In the first thesis author researches an axiom in Logics. The second thesis is Goldbach’s conjecture which abstracts the attentions all over the world; the third thesis shows that In measure theory the numbers sequence converges depends on the nested open intervals not the nested close intervals by the two formulas of the measurable function in real variable function; the fourth thesis author illuminates that the nested theorem is wrong from three different ways (Lebesgue measure, translation transformation and the proving example in the book); the fifth thesis applies a Riemann’s integrable function to discuss the definition of Riemann’s integral; The sixth thesis author obtains the wrong of stealing to change the concept in the proving process which Legesgue measure of countable set is zero. These four thesis discuss the concept from the four different way; the seventh, eighth, ninth thesis focus on discussing continuity axiom; the tenth thesis author applies selectivity axiom to prove that the immeasurable set is wrong, that is to say, the immeasurable set is measurable. If you read the ten theses, you certainly want the attention in front and back of in proper order from the second to the tenth thesis. These theses submit upon International Mathematical Conference that Dictated to Memorial the Professor Hua in Paking on December 18st, 2000; afterward theses submit to Nature Journal in England

• The converse-negative proposition of a true is false
• Goldbach’s conjecture
• In measure theory the numbers sequence converges depends on the nested open intervals not the nested close intervals
• The nested closing intervals theorem is wrong
• The definition of Riemann’s integral is not correct
• The proof of Legesgue’s measure of the countable set is zero quote the two propositions which are conflict
• The digit inverse order mapping and its invariant subset
• The interval [0,1] is a countable set.
• There exists doubts on the proof of Cantor’s continuum hypothesis
• In real variable function theory, the immeasurable set is measurable

Complement explain

Author has set forth some ideas and the recognitions of the concept of infinity and infinitesimal is the base of next proofs in Goldbach’s conjecture, the symbol of “c” is quoted in the nested closing interval theorem is wrong is the number of the points belong to the interval [0,1], that is the cardinal number of the interval [0,1]. cis the maximal number that can be given by mathematicians in mathematical theory today. Since the existence of c, then there exists the number of the rational number belong to [0,1], too. Hence author has given the assumption of the number of all rational number belonged to [0,1]. I hope that someone should pay his attentions on these while he read the theses