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Topic: Matheology § 258
Replies: 2   Last Post: May 1, 2013 4:12 PM

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Alan Smaill

Posts: 1,103
Registered: 1/29/05
Re: Matheology § 258
Posted: May 1, 2013 4:07 PM
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Virgil <> writes:

> In article
> <>,
> WM <> wrote:

>> On 1 Mai, 11:15, Dan <> wrote:
>> > > It is necessary for Cantor's proof. Unless every digit exists on the
>> > > diagonal, the diagonal number is undefined in an undefined list. But
>> > > that is Cantor's claim: forall n : a_nn =/= d_n.

>> >
>> > It exists "as formula" , whether or not you know the formula .

>> There are only countably many formulas. If all diagonals exist as
>> formulas, then all belong to a countable set.

> But if there were only countably many reals, one only needs countably
> many formulas to find the nth digit of the nth real.

In fact WM tells us that there is a single finite description
P(n,m) of the paths through the binary tree such that for every
pair of naturals n,m, P(n,m) characterises the nth digit of
the mth path.

Alan Smaill

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Alan Smaill
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