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Godel numbers 190 35 The fixed-point theorem. Develops logical reasoning analysis problem-solving skills creativity and the ability to think in abstract ways.
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Godels incompleteness theorem 203 36 Recursive undecidability.
. It uses a universal language of numbers and symbols which allows us to communicate ideas in a concise unambiguous and rigorous way. Using mathematical induction on the statement Pn defined as Qm is false for all natural numbers m less than or equal to n it follows that Pn holds for all n which means that Qn is false for every natural number n. Finite and denumerable sets 253.
The course develops important mathematical techniques which are critical to successful. Churchs theorem 216 4 Axiomatic set theory 225 41 An axiom system 225 42 Ordinal numbers 240 43 Equinumerosity. The most common form of proof by mathematical induction requires proving in the inductive step that.
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