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 operation”, the elements in the power set are more than those in its “original set”: the elements in its “original set” are finished, limited, finite, and no-endless while the elements in the power set are unfinished, unlimited, infinite, and endless.
-------the theory of bigger (smaller) cardinality between different “infinite sets” ( such as Cantor’s Theorem, the cardinality of natural number set is smaller than that of real number set,…) has clearly proved another law that any “infinite set” with smaller cardinality can be changed （turned）into a finite set in front of an “infinite set” with a bigger cardinality!
One thing is sure: the discovered defects in fundamental areas of mathematics shall be solved sooner or later.
I would say no, it would mean truncation of an infinite set. However, the opposite, changing a finite set into an infinite one using induction or generalization is easy.
If you allow truncation both are easy.
ie. turn 123 into 123.... is generalization or induction. The opposite is truncation.
Dear Mr. Juan Weisz,
Many people nowadays really do the truncation but they got “less infinite” and “more infinite” things.
Five of my published papers have been up loaded onto RG:
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)
The man who deals with more infinite things, or less is of course Cantor.
The numerable infinity of the integers, has smaller cardinal number than the
non numerable real numbers. You should read him.
Dear Mr. Juan Weisz, thanks!
What is infinite?
Do you think there are really “less infinite” and “more infinite” for the concept of infinite in our mathematics?
Yes, cantor theory is quite credible. Fractions, or rational numbers, are also numerabley infinite.
Finding something in between the numerable and non numerable is a still unsolved problem. Most think there is not.
It is under the category of infinite set theory.
Remove half the elements of a numerably infinite set, and you still have the same number of elements.
Dear Mr. Juan Weisz, thanks!
So, you think that there can be many definitions for “infinite”--------“infinite”, “more infinite”, “less infinite”, “more more infinite”, “less less infinite”, “more more more infinite” “less less less infinite”, “more more more more infinite”, “less less less less infinite”, “more more more more more infinite”, “less less less less less infinite”, “more more more more more more more infinite”, “less less less less less less infinite” and “more more more more more more more more infinite”…?
The restriction for now is between the integers and real numbers.
But I understand the you can get as infinitive as you like.
The mathematicians should know much more than me.
Dear Mr. Juan Weisz, thanks!
It is just because most of mathematicians nowadays didn’t know much about what “infinite” is that we can see so many suspended “infinite related paradoxes” (paradox syndrome complex) in present mathematical analysis and set theory ---------the "thousands--year old huge black clouds of infinite related paradox families over the sky of present classical mathematical analysis" .
In psychology sometimes you think of one thing, but its different(Gestalt)
remove 1/2, 2/3, 3/4,.... elements from 1234....Of course you always have the same number of elements (infinite) You get
1 2 3 4 5 6 7 8 9.....
2 4 6 8 10 12....
3 6 9 12 15....
But this is just the multiplication table!
Dear Mr. Juan Weisz, thanks!
Psychology way is not a scientific one in mathematics because it produces many different definitions for mathematical things-------mathematics is science but not a religion.
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