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 of psychological thing”, even each person can have his/her own definition,
3, mathematicians and physicists see the concept of infinite differently, so we can even have “mathematical infinite and physical infinite”,
. . .
Can we really have infinite definitions for the concept of “infinite”?
According R. Rucker, Infinity is the concept of something that is unlimited, endless, without bound. The common symbol for infinity, ∞, was invented by the English mathematician John Wallis in 1657. Three main types of infinity may be distinguished: the mathematical, the physical, and the metaphysical. Mathematical infinities occur, for instance, as the number of points on a continuous line or as the size of the endless sequence of counting numbers: 1, 2, 3,…. Spatial and temporal concepts of infinity occur in physics when one asks if there are infinitely many stars or if the universe will last forever. In a metaphysical discussion of God or the Absolute, there are questions of whether an ultimate entity must be infinite and whether lesser things could be infinite as well.
The following is a general classifications of infinite: potential infinite, actual infinite; and theological infinite.
Even in mathematics, there is not a simple dichotomy between the finite and the infinite. Opposed to the finite are the potential infinite and the actual infinite. The potential infinite is an extension of the finite, constructible from the finite by some rule or process that is never in fact completed. The actual infinite, on the other hand, is conceived as an actually existing collection of an infinite number of parts. The actual infinite could be regarded as the completion of a process that builds the infinite from the finite. This is the actual infinite of set theory.
God's infinity, however, is not conceived as one of these species of mathematical infinity. Descartes and Leibniz, for example, make a further distinction between the mathematical infinite and what they call the absolute infinite (and which I shall call the theological infinite). The conception of the theological infinite is not a conception of an infinite collection, but rather of the unbounded or unlimited.
We live in a three dimensional world, defined by time and space. ' Infinite' is not finite, therefore boundless,and immeasurable. In physical term, the concept of 'infinity' may be the inverse of the concept of 'zero'. In metaphysical term, human body is finite and mortal; but the soul is dimensionless and immortal.
Dear Dr. Jorge Morales Pedraza and Dr. Jaharkanti Dattagupta, thank you very much for your ideas.
When we discuss the “infinite” concept in our science, “infinite” should include both “infinite big, infinite many” and “infinite small, infinite few”.
Yes, “potential infinite and actual infinite” have been most wildly accepted in our science; we can see it is generally accepted since antiquity, any scientists working in the “infinite related field” are unable to run away from “potential infinite--actual infinite” and have been tortured by the confusion of “potential infinite and actual infinite” ever since:
1, potential infinite: limitless thing, boundless thing, forever developing-changing, without beginning and/or ending, invisible thing, untouchable thing, non-number,…
2, actual infinite: a scientific being of not forever developing-changing, nothing of something, limited unlimited thing, bounded unbounded thing, visible invisible thing, touchable untouchable thing, non-number number,…
What is more, since mathematicians and physicists see the concept of infinite (not only infinity of “infinite big, infinite many”) differently, so can we even have “mathematical infinite and physical 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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