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Questions related from Geng Ouyang
It is generally accepted that the existing limit theory, which would deal exclusively with "infinitesimal number forms", may operate in one of following two ways: （1） During the whole quantitative...
24 November 2020 7,503 3 View
In fact, it is the fundamental defects in the work of “quantitative cognition to infinite things” that have been troubling people for thousands of years. But I am going on a different way from...
19 October 2020 1,130 2 View
(1) An "infinite set" is consisted by a kind of "infinite elements (infinite carriers)" ------- there will be no "infinite set" without "infinite carriers". (2) The unique characteristics (special...
11 February 2020 9,216 3 View
This “world challenging conundrum” focuses on the foundation of present infinite theory system as well as the foundations of infinite related number system and limit theory---------whether the...
19 March 2018 4,098 15 View
The studies to our infinite related science and mathematics history have proved that a new visible and tangible “infinite related mathematical carrier (called ‘infinite mathematical carrier’ or...
15 March 2018 9,080 4 View
How can we define “infinite” and “finite” if we agree with the idea and the operations in Cantor's proofs that many infinite sets in mathematics actually can be proved (turned into) finite...
13 March 2018 7,440 6 View
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...
23 February 2018 4,453 4 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...
18 February 2018 3,904 2 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...
08 February 2018 7,726 7 View
Basing on “potential infinite--actual infinite”, do we have only following three different operating ideas and results of quantitative studying and cognizing on “elements in infinite sets” in...
13 January 2018 4,529 3 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...
11 January 2018 8,369 7 View
The suspended “infinite related paradoxes” in analysis and the “infinite related paradoxes” in set theory used to be studied and discussed separately since ancient times, it used to be regarded...
29 December 2017 5,284 4 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...
21 December 2017 2,839 4 View
We understand from our science and mathematics history, the fundamental defect in present classical set theory disclosed by the members of Russell’s Paradox Family in different periods of time is:...
21 December 2017 6,272 9 View
Just take a subset of the Natural Number Set (2,4,6, ... ,2n, ...) and they map very well on the set of all Natural Numbers (1,2,3,...,n,...). So a lot of (infinite) natural numbers (all of...
20 December 2017 7,743 42 View
（1）Denying the essential differences of infinite set elements’ “special nature, special existing condition, special manifestation and special relationship among each other”, so, elements in all...
14 December 2017 5,643 5 View
Many people agree that we are really able to produce infinite items each bigger than 1/2, or 100, or 1000000, or 100000000000000000000000000000,…by the brackets-placing rule with limit theory from...
23 May 2017 6,012 15 View
It is true that during the “one-to-one correspondence” operation between Real Number Set and Natural Number Set, after the elements in Natural Number Set have been finished up, the elements in...
10 February 2017 8,580 9 View
Following six unavoidable suspended conundrums by newly discovered Harmonic Series Paradox have been troubling us human since antiquity： 1, what are those Un--->0 items in Harmonic Series, are...
23 January 2017 2,478 4 View
The fundamental defects Zeno's Paradox have disclosed are inside mathematics; just see the “debates” in newly discovered modern version of Zeno's Paradox---------Harmonic Series Paradox: 1, Are...
07 December 2016 1,474 11 View
Our science history tells that we human have been arguing and debating on the nature and definition of “potential infinite and actual infinite” for at least 2500 years since Zeno’ time, and there...
22 August 2016 6,835 4 View
Set theory and analysis have brought us human tremendous achievements in our science, but so many suspended “infinite related paradox family members” strongly proved that there have been fatal...
21 August 2016 6,310 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...
31 May 2016 1,152 19 View
At least from Zeno’s time, most people (except Zeno with his creative “actual infinite--potential infinite” related paradox families) have been ignoring a fact that our whole present infinite...
03 May 2016 9,116 13 View
In our present infinite related mathematics theory system, no “infinite things” can run away from “actual infinite” and “potential infinite”. So, are there “actual infinite many (big)” and...
02 May 2016 4,717 14 View
Some people think Un--->0 in Harmonic Series and dx --->0 in calculus are both “actual infinite” while some think they are both “potential infinite”, still some think they can be both in...
22 March 2016 6,224 3 View
We have “big” and “small” in our science and the related numerical cognizing way to universal things around us （one of the mathematical cognizing ways）. So, we have “very big (such as 10001000)”...
21 March 2016 4,432 46 View
As we know, infinite has been defined as “endless, unbounded, unlimited”; but “potential infinite” has been defined as “endless endless, unbounded unbounded, unlimited unlimited” while “actual...
12 March 2016 3,130 12 View
There have been three suspended questions in present classical set theory ever since: 1, the definition of set------should the definition of set concern the nature of elements inside the set? How...
29 January 2016 6,935 15 View
There are “potential infinite” and “actual infinite” in our present infinite related classical science theory system at least since Zeno’s time, so we can not avoid (logically have) “potential...
15 January 2016 4,643 54 View
There have been two suspended questions challenging us human in present classical infinite related science system at least since Zeon’s time: 1, is it unavoidable that we mix (jump between)...
27 December 2015 8,089 24 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...
15 August 2015 1,858 3 View
Why we say mathematically something is more or less, bigger or smaller … than the other （different grade）? One of the main scientific reasons is because of different quantities (not being...
13 April 2015 8,917 65 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...
22 March 2015 9,332 63 View
People believe that 0 (zero) has played different rolls as a kind of special form of number (substantiality) in our science, such as:(1) A kind of reference ------- generator, middle, neutral,...
10 January 2015 4,419 32 View
We focus on the “deep structural relationship” between “nonstandard one” and “standard one”. Let’s exam following facts: 1, as “monad of infinitesimals” has much to do with analysis; nonstandard...
25 December 2014 2,973 36 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...
13 December 2014 4,303 4 View
“Infinite”, “potential infinite”, “actual infinite”, “potential infinitesimal”, “actual infinitesimal”, “potential infinite-big”, “actual infinite-big”, “Infinite related numbers”,…; What are...
19 October 2014 8,318 56 View
If not, “How can we introduce the idea of infinite to students? Its properties, relationship with zero etc?” So, our students will never know what “infinite” is theoretically and practically and...
09 October 2014 4,760 21 View
In mathematics, there is a kind of number carriers with cognizable quantitative properties (such as imaginary number, fuzzy number, infinitesimal variables and monads … in present mathematics)";...
01 January 1970 8,870 0 View
As The First Generation of Infinite Set Theory is based on present classical infinite theory system, contradictory concepts of "potential infinite” and “actual infinite" make people unable to...
01 January 1970 1,431 2 View
We have understood from the studies of infinite related mathematics’ history that present classical infinite theory system is based on the concepts of "potential infinite and actual infinite",...
01 January 1970 1,696 3 View
As "the first generation of infinite set theory" is based on present classical infinite theory system, contradictory concepts of "potential infinite” and “actual infinite" make people unable to...
01 January 1970 3,410 3 View
The fatal defects in the foundations of present science system inevitably lead to the existence of “self-refutation mechanism”. Our 2500 years unsuccessful “infinite relating paradoxes” fighting...
01 January 1970 5,563 4 View
The emergence of the new infinite theory system determines the emergence of the second generation of infinite set theory and the fourth generation of mathematical analysis------- we call present...
01 January 1970 9,477 17 View
01 January 1970 6,123 3 View
In the "second generation of infinite set theory" based on the new infinite theory system, the "infinite carrier theory" is the basic theory for quantitative cognitions and studies of many...
01 January 1970 318 4 View
As The First Generation of Infinite Set Theory is based on present classical infinite theory system, it is bound to be unable to get rid of the confusion of "potential infinite and actual...
01 January 1970 8,874 0 View
The unavoidable fatal defect of “’potential infinite--actual infinite’ confusion” in present classical infinite idea inevitably leads to the unceasingly production of “paradox events” (different...
01 January 1970 6,448 26 View
Because "the first generation of infinite set theory" (Cantor’s set theory) is based on present classical infinite theory system, it is bound to be unable to get rid of the confusion of "potential...
01 January 1970 8,763 8 View
Let’s see following three incoherent situations: (a) During the quantitative cognizing calculation process in dealing with "infinitesimal variables or monads”, all of a sudden someone cries out...
01 January 1970 8,746 1 View
