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William Hughes schrieb:
> For every real number x, there exists a list, L_x such
> that x is a member of L_x
Where do they exist? It is impossible for most real numbers even to
name them. You cannot name or construct more than aleph_0 real numbers.
Nevertheless you insist, that also the other ones, which have no names
and no other identification properties, should have complete lists?
>
> There exists a list L, such that every real number x is
> a member of L.
>
> The first is true, the second is false. There is no way to put
> all the L_x together to get a "countable set of entries"
> (the list L).
But if they existed, then we could put them together. Why can't we
connect in our thoughts all these thought lists such that there is only
one thought list, i.e., the thought list of all thought lists? At least
a square of all thought lists should be possible.
But if you like, you can schematically consider all real numbers by the
infinite binary tree which contains them all represented by a countable
set of nodes and edges. I have shown by a rational relation that the
set of branches (corresponding to real numbers) is not larger than the
set of edges.
Regards, WM
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