Doron Shadmi
Member
Member # 965
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posted 13. February 2004 22:55
No theoretical system can survive if we are not aware to its limitations.
It means that any x input can be only a model(X) output.
Shortly speaking, x=model(X).
Math is first of all a form of theory, therefore any concept that can be used by it is only a model(CONCEPT).
For example, let us take infinity concept.
If INF is infinity itself (= actual infinity) , then inf=model(INF)=potential infinity.
Please look at this model for better understanding:
http://www.geocities.com/complementarytheory/RiemannsLimits.pdf
In this way we first of all aware to our input limitations, which are:
No input = model(EMPTINESS) = lowest limit.
No input = model(FULLNESS) = highest limit.
If we translate this to set's representation then:
{} content = model(EMPTINESS) = lowest limit.
{__} content = model(FULLNESS) = highest limit.
Between these limits ({},{__}) we can find inf=model(INF)=potential infinity, where inf has two input forms:
{.} = singleton, which is a localized element.
{.__.} = non-singleton, which is a non-localized element (connect at least two different singletons).
{.} and {._.} can appear in two basic collections:
Collection {a, b, c} is finitely many elements.
Collection {a, b, c, ...} is infinitely many elements (=inf).
Any non-empty collection which is not a singleton, is an association between {.} and {._.}, for example:
code:
b b
{a , a}
. .
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|___|_
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{a , b}
. .
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|___|
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For more details please look at:
http://www.geocities.com/complementarytheory/CATpage.html
I'll be glad to get your remarks and insights.
Thank you.
Doron
[ 20. February 2004, 12:46: Message edited by: Doron Shadmi ]
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