- #71
Hurkyl
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One additional comment; if a new system includes an old system inside it, then all of the results of the old system must also be results of the new system.
Originally posted by Organic
master_coda,
I am not talking about the second (f: A --> A) I am talking about the meaning of being a collection of infinitely many objects.
So, when A is a collection of infinitely many objects,
its identity map (f: A --> A) = (f: A --> B) , where B is a proper subset of A.
But this is exactly what I clime about the paradox which appears contrary to expectations, and if you read this http://www.geocities.com/complementarytheory/Identity.pdf
I am sure that you will understand my argument.
Originally posted by Organic
Please give another intersting result that using this difference between left and right shifts, thank you.
Edit 1:
I have an idea about this non-symmetric shift.
When we deal with the identity map we don't care about some possible difference that can be between each pair included in the map.
Shortly speaking, in any identity map pairs_possible_difference = 0
In a collection of infinitly many objects A, for any bijective map
between A to some proper subset B of it (or some arbitrary unordered collection of A) pairs_possible_difference > 0 .
Where can I find some paper that deals with what I call pairs_possible_difference?
Edit 2:
I have another idea based on the difference between
pairs_possible_difference = 0
XOR
pairs_possible_difference > 0
Multiplication and Addition are the same only when pairs_possible_difference = 0.
What do you think?
Shortly speaking, in any identity map pairs_possible_difference = 0
In a collection of infinitly many objects A, for any bijective map
between A to some proper subset B of it (or some arbitrary unordered collection of A) pairs_possible_difference > 0 .