Re: infinity

zuhair said:
> To all interested mathematicians:
>
> I have developed a new way of defining and calculating the infinite,
> which escape all the contradictions involved in prior ways of analysis,
> a lot of confusion comes from not discriminating between two very
> different concepts, that of totality and that of infinity.
>
> See My web site: http://zaljohar.tripod.com
>
> read in it :
>
> Articles: Introduction to the infintie calculus
> The Infinite Calculus
> Comparison between Cantor's Transfinite math. and The
> Unitary infinite math.
> Discussions
>
> Anyhow the solution to the problem of the balls is obvious according to
> my system,it is as follows:
>
> If we place the balls horizontally and add them horizontally (
> horizontal arithmetic addition)like below:
>
> [1][2][3][4].......[9][0][11][12][13][14].......[19][0]......................
> = (9/10)w
>
> were w= Omega the smallest infinite real number( not like in Cantor
> were Omega is the smallest transfinite ordinal)
>
> w is the number of terms in a set that has 1-1correspondance with the
> natural number set
> 0,1,2,3,...........
>
> w= 1+1+1+1+...............
>
> In unitary symboles w= |||............
>
> Of coarse in that system : number one = I
> two = ||
> three=|||
> n = |(n)
> zero=0
>
> in unitary symboles the symbole 0 means abscense of exactly one |.
>
> So |0|0|0............ = w/2
>
> in general |(x) 0(n)|(x) 0(n)|(x) 0(n) ............... = w* [x/(n+x)]
>
> (x) on the right of | denotes how much | is repeated, also (n) on the
> right of 0 denotes how much zero is repeated.
>
> Accorgingly since each ball [x] is one in number=| then :
>
> [1][2][3][4].......[9][0][11][12][13][14].......[19][0]......... = |(9)
> 0 |(9) 0 |9 0 .......
>
> = (9/10)w
>
>
> However if we add the balls at a direction different from the direction
> they are placed in
> ( Geometric Addition) as below:
>
>
> [9] [9] [9]...................
> .
> . ...............................
> . = 9w
> [3] [3] [3]....................
> [2] [2] [2]....................
> [1] [1] [1].....................
>
>
> I think that the later is the right result since it is more
> discriminative than the first.
>
> However I also want to mention the traditional Cantorian solution for
> that problem :
>
> According to Cantor the total Cardinal number of balls is the first
> Transfinite Cardinal Aleph-0
> and the total ordinal number of balls is the first Transfinite Ordinal
> w or Omega.
>
> In my mathematics of the infinite the ordinality and the cardinality
> have almost the same
> relationship for finites and infinites with only very differences.
>
>
> I think it is very important very every one who considers himself an
> interested in the mathemactics of the infinite to really read my web
> site carfully.
>
> Zuhair Al Johar
>
>
I tried to print it, but it runs off the side of the page. I don't know if you
can do something about the format of it so it prnts okay. I think your ideas
are not bad, but I caution against considering any kind of smallest infinity,
since subtracting q from an infinite leaves an infinite number remaining. As
far as whether you have 9/10 w or 9w, that depends on whether you have w balls
altogether, or perform w iterations of adding 9 balls. This is where I say that
establishing the value range under consideration is crucial for getting any
kind of accurate results. Anyway, keep up the study. The unary representation
is not a bad approach, but not the only one. Have a nice day.
--
Smiles,

Tony
.

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