Paradoxes in our science have been special scientific contents which are constructed purpersly or unpurpersly to disclose the fundamental defects in certain areas of humans science. Along with humans’ evolution and the expension of our knowledge, our science has been evluting and completing constantly. So, paradoxes have been accompanying our science all the time-------no fundamental defects no paradoxes.
Our science history has proved that the existence of paradoxes in certain area of human science is not only the touchstone for the defects in the very science area (such as the suspended paradoxes in present infinite set theory) but also the strong “metabolism signal” for the related basic theory. And, the “‘infinite related paradoxes’ symptom complex” in some science areas (such as the suspended paradox families in present mathematical analysis and infinite set theory) disclose even more in their special way the ponderance and universality of the fundamental defects in their related science areas -------new scientific basic theories must be constructed to replace those former “paradoxes generating unscientific basic theories” in those very science areas.
Those suspended “infinite related paradoxes” in present mathematical analysis and in set theory used to be studied and discussed separately since ancient times, it used to be regarded that they have been nothing to do with each other. But, if putting all these paradoxes in analysis and in set theory together, we discover immediately that they are in fact forming an “‘infinite related paradoxes’ symptom complex” discloses in its special way exactly the same fundamental defects in different areas of present infinite related science and mathematics. This new idea helps us open up a new way to study and solve those suspended “infinite related paradoxes” in present mathematical analysis and in set theory-------discarding the inevitably confusing concepts of “potential infinite--actual infinite”, developing the new infinite theory system basing on the theory of "abstract infinite law--abstract infinite law carriers" and looking for the scientific foundation for mathematical analysis and in set theory.
Paradoxes in mathematics are bundled to very simpler rules than you named them, too.
About 2,500 years we follow the rules for the signs (prefixes) by multiplication. After the lecture of `Alberto A. Martinez, negative math´ we could´t definitely say whether `+ by +´ should get `+´ or `–´.
Following that the square-root could not lead to both the factors which produce a negative result.
Your list adding: math has to be reformed. Thanks Geng Ouyang!
Thank you very much for your ideas dear Mr. Peter Kepp，
Studies on the infinite related mathematics history have proved that it is the inevitable fundamental defect of “’potential infinite--actual infinite’ confusing” caused by the absence of systematic theory of “scientific carriers” that decides any areas in present infinite related science (including mathematical analysis and set theory) are unable to escape from the influences and constraints of such fatal defect, unable us to conduct the quantitative cognizings scientifically to “infinite related mathematical things”. So, many infinite related paradox families (symptom complex) in present mathematical analysis and set theory have been inevitably produced. Although many ways to solve this “paradoxes symptom complex” have been invented in our infinite related mathematics (such as Standard Analysis, Nonstandard Analysis, Type Theory, Model Theory, ZFC ) since Zeno 's Achilles and Tortoise Paradox, non of them is able to solve the real trouble of “’potential infinite-actual infinite’ confusing”--------The Second Mathematical Crisis and The Third Mathematical Crisis are unsolvable at all in present infinite related science and mathematics basing on classical infinite theory system. The systematic studies and development of “the idea and theory of ‘scientific abstract law--the carriers of scientific abstract law’” (especially the systematic studies and development of “the idea and theory of ‘the carriers of science’”) will fill in a blank in the foundation of Logic Theory and open a new way and a new working field for our further studying and cognizing on Logic (the relation laws among things in the universe).
“The natural metabolism law (mechanism)” is governing the whole life process of any “alive things” in the world. Humans’ mathematics is an alive thing concomitant humans, it metabolized and evolved before, it is metabolizing and evolving now, it will metabolize and evolve in the future and, those unscientific things must be out while some scientific things must be in whenever the time is ripe. Having been suffering from the tormenting of “‘potential infinite--actual infinite’ confusing”, we should look for the new working idea and jump out of the “‘potential infinite--actual infinite’ confusing” abyss. The emergence of the new infinite theory system and the revolution in the foundation of present mathematical analysis and set theory decide the emergence of the Fourth Generation of Mathematical Analysis and the Second Generation of Set Theory. Only discarding the unscientific concepts of “potential infinite, actual infinite” in present infinite theory system and construting the new infinite theory system basing on the scientific concepts of "abstract infinite law--abstract infinite law carriers", studing and developing the systematic new "’scientific carriers--scientific carriers treating’ theories", can we fairnessly and justifiably conducting the quantitative cognitions to “infinite related mathematical things” with the systematic theory of “scientific carriers”, solving the fundamental defects disclosed by the obstinate “infinite paradoxes symptom complex” theoretically and operationally to dispel the thousands years suspended black cloud of “infinite related paradox families” over the sky of present mathematics and science.
Yous,
Geng Ouyang
Thank you very much for your ideas dear Mr. Joseph Lurie,，
If putting all the suspending paradoxes in analysis and in set theory together, we discover that they have disclosed exactly the same fundamental defects in present infinite related science and mathematics.
No one in the world so far has ever studied the suspending infinite related paradoxes this way, that is why I create the new term of “‘infinite related paradoxes’ symptom complex” to express a 2500-year intractable disease in present infinite related science and mathematics.
Five of my published papers have been up loaded onto RG to answer such questions:
1，On the Quantitative Cognitions to “Infinite Things” (I)
2，On the Quantitative Cognitions to “Infinite Things” (II)
3，On the Quantitative Cognitions to “Infinite Things” (III)
4 On the Quantitative Cognitions to “Infinite Things” (IV)
5 On the Quantitative Cognitions to “Infinite Things” (V)
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