CS120: Lecture 15

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CS120 Lecture 15

• MP Johnson
• Hunter
• mpjohnson_at_gmail.com

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Claims

• Some infinities are larger than others.
• Some problems are unsolvable.

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Infinite sets

• Equinumerous sets
• N, Z, squares, primes, Q / cross-product, graph
  paper
• R, 0,1
• Self-reference
• Smullyans brother
• Gmail
• Barber
• Set of all sets
• non-self-describing
• Diagonalization
• R / P(N)

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Undecidability

• Decision problems
• Primality
• 3-colorability
• Has TSP ltk
• Pgms either halt or loop
• Von Neuman pgms are data
• Given H, can define D(x) down, if x(x) up
• up, if x(x) down
• Assume H is decidable
• Then D(D) down, if D(D) up
• up, if D(D) down ??