Cantor's Diagonal
- From: "zuhair" <zaljohar@xxxxxxxxx>
- Date: 29 Nov 2005 11:17:15 -0800
Hellow everyone.
I don't remember Cantor's diagnal very well , but from what I collect
I think it is like that.
If R' = { r1, r2 , r3,...............} is a coutable set of real
numbers [0,1]
r1= 0.d11 d12 d13 d14..............................
r2= 0.d21 d22 d23 d24 ...............................
..
..
..
were dij= 0 or 1.
Then there is always a number ro= 0.k1k2k3k4....................
were k1 <> d11 , k2<>d22 , k3<> d33,.....................
or
ki = 1- dii
so ro do not belong to R'.
But ro belong to the set of real numbers R.
Therefore R is not countable.
But this is silly!
since Aleph-0 + 1 = Aleph-0
Zuhair
.
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