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Results tagged with examples
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user 50073
For questions requesting examples of a certain structure or phenomenon
21
votes
Request for examples: verifying vs understanding proofs
Many of the best examples involve the proof of an existential statement that requires constructing a complicated witness for it. … These are examples from basic mathematics, but I hope it demonstrates how an existential statement might have a proof that does not in itself provide any understanding of the proof, in the same way you …
10
votes
Taking a theorem as a definition and proving the original definition as a theorem
Example 1: In some textbooks, the trigonometric functions are defined via geometry. The advantage is that it is simpler to understand, but the disadvantage is that it is difficult to make completely r …