WM
2016-12-05 08:40:43 UTC
[snip]
)OK. But the identification step is essential in the Cantor
)proof. There is a step in the proof that says, "for if you
)claim that my number is at position x, then I will assert that it
)differs from your number in the x'th digit."
)
)So what if I simply claim that the number is somewhere in the
)list but that if I were to tell you where it was that would lead
)to a contradiction? It seems that the Cantor proof, at least in
)that form, might only be proving that the position on the list
)cannot be made definite.
You cannot claim to have made a list without being able to specify where
it is. Or to put it another way - you are saying that the number is in
there, without there being a way to find it. But there -is- a way to
find it. It must be in -one- of the slots. So we just start scanning the
list. If it is -in- the list, then we will encounter it. The only
numbers which result in ifinitely scanning the list are numbers -not- in
the list. So if it is in the list, we -can- find it.
That is the common conclusion.)OK. But the identification step is essential in the Cantor
)proof. There is a step in the proof that says, "for if you
)claim that my number is at position x, then I will assert that it
)differs from your number in the x'th digit."
)
)So what if I simply claim that the number is somewhere in the
)list but that if I were to tell you where it was that would lead
)to a contradiction? It seems that the Cantor proof, at least in
)that form, might only be proving that the position on the list
)cannot be made definite.
You cannot claim to have made a list without being able to specify where
it is. Or to put it another way - you are saying that the number is in
there, without there being a way to find it. But there -is- a way to
find it. It must be in -one- of the slots. So we just start scanning the
list. If it is -in- the list, then we will encounter it. The only
numbers which result in ifinitely scanning the list are numbers -not- in
the list. So if it is in the list, we -can- find it.
It has lead to over 100 years of set theory.
It is wrong.
When scanning the list we will always remain in a domain that is preceded by a finite number of slots but is succeeded by an infinite number of slots.
This does never change - in infinity.
Regards, WM