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Questions related from Geng Ouyang
In fact, this problem has been deeply troubling us: 1. Are “infinite sets” in present set theory “actual infinite sets” or “potential infinite sets”? 2. Are infinite elements in infinite sets...
11 November 2018 5,961 4 View
1, When “n--->infinity”, is there only one “1/n--->0” item or are there many “1/n--->0” items or are there infinite “1/n--->0” items in Harmonic Series? 2, How should such “1/n--->0 mathematical...
03 March 2018 8,464 1 View
Zeno’s Achilles--Turtle Race Paradox is the greatest paradox: 1, it has never been solved and suspended for more than 2500 years. 2, it is a huge paradox family with so many family members. 3,...
03 March 2018 3,299 1 View
Someone suggests a new way to create infinite numbers each greater than any positive constants from those Un--->0 items in Harmonic Series and turn the Un--->0 infinite Harmonic Series into a “Vn...
03 March 2018 6,642 2 View
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...
02 February 2018 7,455 5 View
The fundamental defects of “potential infinite and actual infinite” confusions in present classical infinite set theory have been making us humans unable to study and cognize scientifically the...
02 February 2018 1,568 11 View
The emergence of new infinite system (new 'infinite' idea, new number system and new limit theory) determines the production of "new mathematical analysis". The mathematical analysis based on the...
02 February 2018 4,530 7 View
4, Are “infinite sets” in present set theory “actual infinite sets” or “potential infinite sets”? 5, Are infinite elements in infinite sets “actual infinite many” or “potential infinite many”? If...
02 February 2018 8,235 4 View
The emergence of new infinite system determines the production of "new infinite set theory"--------The infinite set theory based on the classical infinite system is called "classical infinite set...
02 February 2018 8,938 8 View
We understand from the infinite related mathematics history that in present classical mathematics (such as classical mathematical analysis and classical set theory) basing on classical infinite...
02 February 2018 7,908 3 View
Our infinite related science history has proved that present classical infinite theory system is the foundation of present classical infinite set theory, so all the contents in present classical...
01 January 2018 2,859 53 View
We understand from our infinite related science history that in present classical infinite related science system, it has been admitted that the concept of infinite is composed by both “potential...
01 January 2018 966 8 View
Of cause in present infinite related mathematics, Russell did not go wrong in Russell’s Paradox at all. Because the exactly same mechanism of Russell’s Paradox (the “prodution line” of looking for...
01 January 2018 7,561 13 View
The fundamental defects in present classical infinite related science system have decided the barber paradox (one of the members of Russell’s Paradox Family) is really an unavoidable and...
12 December 2017 4,272 5 View
If “Yes”, why we have totally different operations on them? If “No”, what are the differences and how to treat them differently and why? Lacking systematic cognition to “infinitesimal” by the...
11 November 2016 4,952 2 View
We have at least two different definitions of “infinite” (“actual infinite” and “potential infinite”) since antiquity, and these two different “infinites” with different natures unavoidably become...
05 May 2016 9,388 20 View
There have been two opposite phenomenon about the definition for infinite in present classical infinite related science system: (1) plenty of different mathematical definitions for infinite and...
03 March 2016 4,211 9 View
Infinite with its not-knowing-what “potential infinite--actual infinite” are right there in our science ever since and none of the “infinite things” in present classical infinite related science...
02 February 2016 5,474 3 View
It is believed that there are the bijection relationships between Infinite Natural Number Set and Infinite Rational Number Set, but following simple story tells us that Infinite Rational Number...
01 January 2016 9,363 94 View
Limit theory is a very useful cognizing tool in human science. It treats “infinite number forms”. But its foundation is empty: 1, what kind of “infinite number forms” it treats-------potential...
01 January 2016 6,269 43 View
We call a certain day 2015-12-1 "H" and another day 2015-12-10 "b", "H" ends at 2015-12-1 but has no beginning; and "b" with a beginning at 2015-12-10 and infinitely going up. Now the problem is:...
12 December 2015 5,924 25 View
In my humble view point, my dear RG friends, posts with frank ideas and view points are far more valuable, reasonable, scientific, constructive and fruitful than downvotings (especially some...
12 December 2015 9,197 14 View
Many people believe that there is never be the Achilles--Turtle Race Paradox in our science at all because it can be solved either by middle school’s “series calculating skill” or “practical...
10 October 2015 6,797 13 View
Our science history since Zeno’s time 2500 years ago tells us clearly: there are serious fundamental defects in present infinite related classical science theory system-------both in philosophy...
09 September 2015 7,672 5 View
Since “infinite” concept came into our science, the “infinite” related concepts and theories such as “potential infinite”, “actual infinite”, “countable infinite”, “uncountable infinite”,...
09 September 2015 2,972 86 View
1, There are many knowers in this world (such as human, monkey, fishes, bees,…), each knower has their own general cognizing ways decided by the species’ biological structure. We call these...
09 September 2015 4,148 44 View
As a re--cognizing fruit to certain knowledge system, paradox in our science system is a kind of amazing treasures closely related to the philosophy of science. In a special way, it purposely...
08 August 2015 9,283 2 View
The fact is: theoretically, the present science theory system has really proved the divergence of Harmonic Series; but practically, Harmonic Series is impossible to be divergent because it is...
08 August 2015 4,007 4 View
The following proof (given by Oresme in about 1360), very elementary but important, can be found in many current higher mathematical books written in all kinds of languages. 1＋1/2 ＋1/3＋1/4＋．．．＋1/n...
03 March 2015 8,290 16 View
1, philosophy of physics once placed a significant role to solve defects in the foundation of physics disclosed by paradoxes. 2, the existing fundamental defects (syndrome of "potential...
03 March 2015 9,502 63 View
Some people say both mathematics and philosophy are not science, because they deal with purely abstract entities. Still some others say both mathematics and philosophy are science, because the...
03 March 2015 9,108 25 View
People may have different names for ”the infinite related very small numerical things (infinitesimals)”, it doesn’t matter what they are called, they are there in our mathematics, but what are...
01 January 2015 8,766 71 View
“Potential infinite” and “actual infinite” are really there in our mathematics and science, but it seems very difficult to understand and express these two concepts clearly and logically ever...
01 January 2015 4,436 69 View
There are two “reasonable” limit operations in convergent- divergent proof of Harmonious Series: 1＋1/2 ＋1/3＋1/4＋．．．＋1/n ＋．．． （1） =１＋1/2 ＋（1/3＋1/4...
12 December 2014 494 5 View
No mathematics without numbers; so, we have many different kinds of numbers in our mathematics to help us cognize all kinds of things in universe. We have many different kinds of number forms: 0...
12 December 2014 7,696 59 View
This work will help us re-understand the essences of the three schools and have a better understanding of “what mathematics is”-----to improve our fundamental researches especially in the infinite...
11 November 2014 6,767 4 View
The problem disclosed by Zeno’s Paradox is still there and the exactly same idea is still working well. Let’s see one of the modern versions of Zeno’s Paradox1＋1/2 ＋1/3＋1/4＋．．．＋1/n ＋．．． ...
09 September 2014 9,916 6 View
Will the infinite related mathematical paradox families keep challenging us human for another 2500 years”?
01 January 1970 5,107 6 View
1 If “X--->0 number forms” are infinitesimals, are they “potential infinitesimals” or “actual infinitesimals” and why? If they are “potential infinitesimals”, how to cognize them...
01 January 1970 5,613 1 View
Different people may have different experiences on it, would you please tell what yours is？ New ideas and treating skills may be discovered and developed from the studies to those problems.
01 January 1970 3,867 8 View
The mathematical analysis based on the classical infinite system is called "classical mathematical analysis", and the mathematical analysis based on the new infinite system is called "new...
01 January 1970 8,090 1 View
The biggest mathematical unsolvable paradox means longest time duration and vastest relating fundamental areas.
01 January 1970 4,640 1 View
It is a law in our present classical “actual infinite--potential infinite” based mathematics that the cardinality of any power set is greater than its “original set” because during the “mapping...
01 January 1970 5,689 14 View
Studying our infinite related science history, we can see so many different definitions for the concept of “infinite” are accepted: 1, potential infinite--actual infinite, 2, “infinite is a kind...
01 January 1970 3,506 4 View
So many people say “infinite thing is not a number”, but we are able to take very freely all the infinite things (such as infinities and infinitesimals) as numbers in the field of analysis and set.
01 January 1970 6,708 10 View
Working in classical infinite theory system with the fundamental defect of “’potential infinite--actual infinite’ confusion”, any things in mathematics relating to “infinitesimals, infinities,...
01 January 1970 6,502 5 View
(1) In mathematics, among the various "infinite related number forms with cognizable quantitative properties (such as infinitesimal variables and monads in present classical mathematical...
01 January 1970 828 2 View
