# Tag Info

### Computation of reals: floating point vs TTE vs domain theory vs etc

I work in real-number computation, and I wish I knew the real answer. But I can speculate. It's a sociological problem, I think. The community of people who work on exact real arithmetic consists of ...
Accepted

### A definition of computable numbers that requires to "wait an infinite amount of time" to get the correct result; how to make this precise

This is not a research-level question, but since the general level of interest seems high, here is an answer. I cannot guess from your question whether you're shooting for something that will result ...

### A definition of computable numbers that requires to "wait an infinite amount of time" to get the correct result; how to make this precise

How about, $x\in[0,1]$ is computable if there is a TM $M$ which, on input $n\in\mathbb{N}$, prints the first $n$ digits of the decimal expansion of $x$ and then halts. Edit (13-Jul-2021). This ...

### A definition of computable numbers that requires to "wait an infinite amount of time" to get the correct result; how to make this precise

The standard solution is to require write only tape if you want to use TTE. Obviously you can have RW work tapes. Another solution is information theoretic (domain theory) and says that you get ...
I guess I have an alternative solution. Let $f :\subseteq \Sigma^{\omega} \to \Sigma^{\omega}$ be computable. Define $$h(u) = v \mbox{ iff } f(u\Sigma^{\omega}) = \{v\} \mbox{ with u minimal}$$ ...