Computability Theory

[mellow cairn]

Hi, I was trying to do this question and I understand how the function is computable but I don't know how I'm supposed to write it down to show that it is. When I looked at the mark scheme it just gave a brief explanation about the question in 1-2 sentences. Could someone tell me how can i write it down to show that the function is computable?

Question:

Assume that we have an enumerated list of computable functions: f0, f1, f2, ..., fi, ... Show that the following function is computable: h(x) = 1, if fx halts on input x, otherwise loops forever.

[drowsy pollen]

👋 Welcome to your Help Thread!

Hey @mellow cairn, Thanks for sharing your math problem with us. While you wait for a Helper to help you, we want to share some vital information with you.

​

● Please take a moment to read the helpee guidelines. This will make sure that your post follows the helpee rules of our community.

​

● Please don't ping <@&775784618955505685>, <@&1283689826742440016>, <@&819616364188139550>, or <@&624327278137966593> for help because their job is to take care of the server's administrative tasks, not to answer queries directly. However, if you have a problem with how a Helper is acting, you can ping a Helper Moderator.

​

● It's always very useful if you can show us the work you've done so far. This makes it easier for our Helpers to find mistakes and help you get to the right answer.

Once you've got your answer and you're all set, you can close this thread by typing +close, and then you can click the Thank buttons to show your Helper some appreciation.

[mellow cairn]

+close

[drowsy pollen]

Do you still want to close your help request?

No eligible helpers were found in this thread. You can still close this post if you don't require helper any longer.