[wizeman]

Also, I don't quite understand what the program QQ is.

Q is a program that takes one input P.

But then you said "QQ is a program which executes Q with itself as input".

So in the program QQ, the first Q uses the second Q as input, but what does the second Q use as input?

[vladsotirov]

The second Q needs no input because it is not executed: its source code is used as input for the first Q.

[wizeman]

> The second Q needs no input because it is not executed: its source code is used as input for the first Q.

But Q is the source code of a program that needs an input.

How would you determine if Q halts or not, if you don't give it an input?