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 (2) no mathematical definition for infinite.
On the one hand, we really have had many different mathematical definitions for just half of the infinite: infinities (infinite bigs) in set theory such as “super (higher, more, less…) infinite, super (higher, more, less…) unbounded, super (higher, more, less…) unlimited, super (higher, more, less…) endless,…”, the plenty of non-self-justification “half definition” for infinite which is nothing to do with infinitesimals strongly prove that we human in fact are unable to know how to have mathematical definition for “infinite” at all------it is impossible to have mathematical definition for “infinite” in present classical infinite related science system.
On the other hand, we really have had many different mathematical definitions for another half of the infinite: non-number infinitesimal variables, actual infinitesimals,… in standard and non-standard analysis, but those suspended infinitesimals related paradoxes (the 2500—year suspended black cloud over mathematical sky), especially the newly discovered Harmonic Series Paradox in present classical infinite related mathematics make us have to admit that till now we human in fact are unable to know how to have mathematical definition for “infinite” at all------it is impossible to have mathematical definition for “infinite” in present classical infinite related science system.
It is the time for us human to work at the integration of mathematical definition for “infinite” now?!
Dear Dr. Peter Breuer, thank you.
I found Dr. Vinoo Cameron and me talk about “mathematical definition for infinite” in quite different directions.
Thank you again dear Dr. Peter Breuer for your recommendation.
Best egards,
Geng
We have “big” and “small” in our science and the related numerical cognizing way to universal things around us. So, we have “very big (such as 10001000)” and “very small (such as 1/10001000)”, “extremely big” and “extremely small”… in mathematics. When “infinite” came into our science and mathematics, we naturally and logically have “infinite big-----infinities” and “infinite small-----infinitesimals”.
When we study Cantor’s work, we can find that he is really a great mathematician who contributed greatly to some work in the numerical cognizing of “infinite big-----infinities” related applied mathematics. But he neglect the important portion of another half------ the field of “infinitesimal” numerical cognizing and even rejecting “infinitesimal”; that is why I call Cantor’s infinite theory “half infinite” in my papers. But this is not Cantor’s fault, it is because of the deep rooted defects in present classical “multi--infinite--definition” related science theory system------- we human in fact don’t have mathematical definition for “infinite”.
One should bring in two definitions for infinite. One should be called relative infinite with a different symbol, and the other the absolute infinite.When we connect the abstract truth to the physical truth we can cognize, there is always a convenience factor varying to the stretch of human imagination. Nice question to dwell on to stumble on the mysterious to unlock further secrets.
Dear Dr. Sundaresan Muthuswamy, thank you.
But the problem is difficult to know whether the “infinite things” you are treating “relative infinite” or ”absolute infinite” and this has been an endless debate ever since. The newly discovered Harmonic Series Paradox is a most typical example.
Best egards,
Geng
@Geng Ouyang
Thank you sir.. I hope some time later could get some views to pass on to you.
This question posed links philosophically to the desires and aspirations in humans and in what frame of mind is one discussing. Straightforward definition is an impossibility just as the limits of human thinking.The real life situations keep changing and advancing all from a collective effort and a single individual is far from the whole. collecting the whole lot and finding a solution seems to be trivial as none know the real value of it.
kind regards,,
sundaresan
Dear Dr. Sundaresan Muthuswamy, thank you.
You are right we are unable to have a definition for things in our science permanently because all the things in our science also follow the law of metabolism along with us human. But we improve things in our science all the time and that is why we are working so hard at “unscientific things in present classical infinite related theory” to dispel “the 2500 years old huge black cloud of infinite related paradoxes over mathematics sky”.
Best regards,
Geng
New philosophical view merging infinity to imaginary number
Article New philosophical view merging infinity to the imaginary number
Dear Dr. Salah A. Mabkhout, thank you.
Very happy to have a chance to know your work on infinite and thank you for sharing with me your ideas; I hope your work can be of some help to the mathematical definitions for infinite.
Dear Dr. Salah A. Mabkhout, do you agree that infinite can be divided into “potential infinite--actual infinite”, and we can have many mathematical definitions for infinite?
Sincerely,
Geng
Five of my published papers have been up loaded onto RG to answer such questions:
1，On the Quantitative Cognitions to “Infinite Things” (I)
https://www.researchgate.net/publication/295912318_On_the_Quantitative_Cognitions_to_Infinite_Things_I
2，On the Quantitative Cognitions to “Infinite Things” (II)
https://www.researchgate.net/publication/305537578_On_the_Quantitative_Cognitions_to_Infinite_Things_II
3，On the Quantitative Cognitions to “Infinite Things” (III)
https://www.researchgate.net/publication/313121403_On_the_Quantitative_Cognitions_to_Infinite_Things_III
4 On the Quantitative Cognitions to “Infinite Things” (IV)
https://www.researchgate.net/publication/319135528_On_the_Quantitative_Cognitions_to_Infinite_Things_IV
5 On the Quantitative Cognitions to “Infinite Things” (V)
https://www.researchgate.net/publication/323994921_On_the_Quantitative_Cognitions_to_Infinite_Things_V
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