Assuming "D" is a set of sequences of natural numbers with the property that for any sequence of natural numbers "s" there exists a sequence "d" in the set "D" and a number "n0" from the set of natural numbers such that d(n)>s(n) for any n>n0.

Prove that any such set D is uncountable.

Can anyone help me? I have no idea how to prove this.

## Set Theory Question

**Moderators:** gmalivuk, Moderators General, Prelates

### Re: Set Theory Question

Assume, for contradiction, that D is countable, so that you can list the elements of D as something like this:

1 -> 1, 2, 3, 4, 5, ...

2 -> 200, 10, 5, 8, 9, ...

3 -> 88, 90, 2, 4, 6, ...

...

Working "diagonally", find a sequence whose tail eventually gets bigger than all of these.

1 -> 1, 2, 3, 4, 5, ...

2 -> 200, 10, 5, 8, 9, ...

3 -> 88, 90, 2, 4, 6, ...

...

Working "diagonally", find a sequence whose tail eventually gets bigger than all of these.

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