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Introduction E9F5FC
Questions FFFFC0
Software
- Study the proofs of famous theorems.
- How are the six methods of proof related to the ways of figuring things out? Study examples of proofs and of problem solving.
- Why are there so many ways of solving the Pythagorean theorem?
Mathematical induction can be thought of as a proof by contradiction where we have organized the conditions in an infinite sequence and we are looking at the first one to fail and proving that it doesn't fail.
Notes
- How is substitution, as a method of proof, related to lamba calculus, and construction?
- Does induction prove an infinite number of statements or their reassembly into one statement with infinitely many realizations? It proves the parallelness of intuitive meaningful stepped in and formal stepped out.
- Mathematical induction - is it possible to treat infinitely many equations as a single equation with infinitely many instantiations? Consider Navier-Stokes equations.
- Relate methods of proof and discovery, 3 systemic and 3 not.
- Induction step by step is different than the outcome, the totality, which forgets the gradation.
- Mathematical induction - is infinitely many statements that are true - relate to natural transformation, which also relates possibly infinitely many statements.