1.11 Infinite Sets | 1.11 Infinite Sets | Unit 1: Proofs | Mathematics for Computer Science | Electrical Engineering and Computer Science

<The Halting Problem: Video [Optional]
1.11.1Cardinality: Video
1.11.2Cantor, Schroeder-Bernstein
1.11.3Countable Sets: Video
1.11.4Cantor's Theorem: Video
1.11.5Cantor's Diagonal Argument
1.11.6Countable and Uncountable Sets
1.11.7The Halting Problem: Video [Optional]
1.11.8Halting Problem Basics [Optional]
1.11.9Russell's Paradox: Video
1.11.10Russell's Paradox [and ZFC optional]
1.11.11Set Theory Axioms: Video [Optional]
1.11.12Set Theory Axioms [Optional]
>Russell's Paradox: Video

Halting Problem Basics [Optional]

The Halting Problem

asks whether a given computational procedure halts on a given input or not.

can be solved by diagonal arguments.

is undecidable - which can be proven by contradiction.

requires a computational procedure that outputs only computable strings, but since the domain for the outputs is \(\{0, 1 \}^\omega \), there are uncountably many noncomputable strings.