Re: Computable functions/reals.

On Aug 23, 4:30 am, David C. Ullrich <dullr...@xxxxxxxxxxx> wrote:


If you assume the input is always a natural
number then the natural numbers are computable.
All you need is a TM that always returns "True".
You don't even need to read the input.

That's correct. And hence, by definition,
the natural numbers are a recursive set.

We assume the natural numbers are
computable by defining the input to always
be a natural number.

So, we decide if a string is a natural number
when we put the representation on the
input tape. The computer justs trusts
our judgement.


But here you're still just spouting nonsense.
Any string read by an actual computer in
finite time is finite. We're not talking about
that - when we talk about Zeno machines
we're _assuming_ it can do infinitely many
things in finite time.

Even if we assume a computer can perform
an infinite number of operations, it can not
read an infinite tape one character at a time.

I have given a proof of this and no one has
pointed out any error in my proof.

If even an infinitely fast computer can't read
certain "finite" tapes then there exists
natural numbers too large to be read by
any sequential computer and the
natural numbers are not computable
(or even recursively enumerable).


Russell
- 2 many 2 count
.

Relevant Pages

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  • Re: No Set Contains Every Computable Natural
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