Re: abundance of irrationals!)


mueck...@xxxxxxxxxxxxxxxxx wrote:

> Then consider this list 2 please:
>
> .
> 0 1
> 0 1 0 1
> 0 1 0 1 0 1 0 1

Does this mean 0.01, 0.0101, 0.01010101, ...?

> and read from top to bottom (like the Chinese do or like we do in
order
> to read the diagonal number of a list).

I don't understand what you mean. What is the first number
in this list? What is the second?

> Then you find ALL the bits of 1/3 = 0.010101... in the positions
> 1,2,3,6,11,22,...

A number x being in your list means that there is m
such that the m-th number in your list is x.
If you want to claim 1/3 is in your list, then it
must be associated with A PARTICULAR VALUE of m.
What value is that? I see you have a sequence of numbers
which you claim are associated in some way with 1/3.

So what? {1,2,3,6...} is not a position. If 1/3 is
in your list, it occurs at a position. There is no
other meaning of "in the list."

> The recursive definition of that sequence a_n (with n
> the line number and a the position in the line) is

What? There's only one index here, n. What is the notation
for "the 17-th digit of the 4-th number"? Is it a_17?
What about "the 17-th digit of the 100-th number"? Is it
also a_17? I have a problem with your notation.

> a_1 = 1 (Position of the first 0 after the point)
> a_n = 2*a_(n-1), if n is even,
> a_n = -1 + 2*a_(n-1), if n is odd.

Are you saying that a_n is the value of the n-th digit
for EVERY number in your list?

That doesn't make sense. Your recursion rule says:

a_1 = 1
a_2 = 2
a_3 = 3
a_4 = 6
a_5 = 11
a_6 = 22

How is this related to your list? What is the first
number in your list? What is the second? What is the
fifth?
- Randy

.

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