Template: Well-Ordering Proofs
Stating the template for a well-ordering proof steps would be adequate to give general explanation of its definition;
- Define the set, C, of counterexamples to P being true
- Use a proof by contradiction and assume that C is non-empty
contradiction definition:
a form of proof that establishes the truth or validity of a proposition by showing that the proposition's being false would imply a contradiction
- By the well ordering Principle, there will be a smallest element(introduced a new variable), n in C.
- Reach a contradiction (somehow) - often by showing how to use n to find another member of C that is smaller than n.
- Conclude that C must be empty, that is, no counterexamples exist.
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