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David R Tribble wrote:
> zuhair wrote:
> > The following introduces the concept of funcitonal numbers in a more
> > standard manner.
> >
> > see http://zaljohar.tripod.com/Operators.txt
>
> There are already standard methods for cardinal arithmetic.
> You might want to read up on:
>
> Fields:
> en.wikipedia.org/wiki/Field_%28mathematics%29">http://en.wikipedia.org/wiki/Field_%28mathematics%29
> mathworld.wolfram.com/Field.html">http://mathworld.wolfram.com/Field.html
>
> Rings:
> en.wikipedia.org/wiki/Ring_%28mathematics%29">http://en.wikipedia.org/wiki/Ring_%28mathematics%29
> en.wikipedia.org/wiki/Division_ring">http://en.wikipedia.org/wiki/Division_ring
> mathworld.wolfram.com/Ring.html">http://mathworld.wolfram.com/Ring.html
>
> Cardinal arithmetic:
> en.wikipedia.org/wiki/Cardinal_number#Cardinal_arithmetic">http://en.wikipedia.org/wiki/Cardinal_number#Cardinal_arithmetic
> mathworld.wolfram.com/CardinalNumber.html">http://mathworld.wolfram.com/CardinalNumber.html
> mathworld.wolfram.com/CardinalAddition.html">http://mathworld.wolfram.com/CardinalAddition.html
> mathworld.wolfram.com/CardinalMultiplication.html">http://mathworld.wolfram.com/CardinalMultiplication.html
> mathworld.wolfram.com/CardinalExponentiation.html">http://mathworld.wolfram.com/CardinalExponentiation.html
>
> Ordinal arithmetic:
> en.wikipedia.org/wiki/Ordinal_arithmetic">http://en.wikipedia.org/wiki/Ordinal_arithmetic
> mathworld.wolfram.com/OrdinalNumber.html">http://mathworld.wolfram.com/OrdinalNumber.html
> mathworld.wolfram.com/OrdinalAddition.html">http://mathworld.wolfram.com/OrdinalAddition.html
> mathworld.wolfram.com/OrdinalMultiplication.html">http://mathworld.wolfram.com/OrdinalMultiplication.html
> mathworld.wolfram.com/OrdinalExponentiation.html">http://mathworld.wolfram.com/OrdinalExponentiation.html
This is not the subject of my post.
I am talking about functional numbers which are the integers and
rationals, and irrationals, and I am not concentrating on the ordinary
algebra we know about them. The subject of this article is to get rid
of unwanted numbers? like 1/0 , 0/0 ,w-w,w/w,etc....., by defining
integers and rationals as Functions rather than as Relations between
subsets of cardinals and integers respectivelly .
What is writtin in Introduction to mathematical philosophy doesn't
exclude these(ie,1/0 , 0/0 ,w-w,w/w,etc.....) from being rationals or
integers, but my correction of these definitions does this job.
>From another hand those who like to build an algebra for these numbers
then this article tells them that they can do this. What was for a long
time thought to be something that elude any human attempt to define
them ( that is 0/0,1/0,w-w,w/w,....) this article tells you that they
can be defined easily using set theory, even algebra of them can be
defined.
And this algebra I call it The Algebra of Dominance.
Try to read this article carefully, since it is clear that you confused
it with another subject that is the subject of cardinal and ordinal
operators, which has nothing to do with this article.
Zuhair
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