The diagonal argument in Turing's halting problem proof yields a contradiction within the formal model alone, so the mathematical result stands independently of any claim about informal computation.

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Alan Turing(the philosopher/scientist being referenced): A British mathematician who pioneered computer science and artificial intelligence; he's famous for asking whether machines can think.
Diagonal argument(Computability theory and set theory): A method of constructing a mathematical object that differs from every member of a given enumeration by differing from the nth member on input n, used here to show a set escapes Σ⁰ₙ-definability
Formal model(logic and theoretical computer science): A mathematical or logical system created to represent and study how something works, using precise rules and symbols rather than real-world messiness.
The halting problem(as a theoretical problem that seemed pointless but became foundational to computer science): A famous question Turing asked: 'Can you write a set of instructions that can tell whether any other set of instructions will eventually finish running or keep going forever?' The answer turns out to be no—it's impossible.

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