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Existence proofs
Applying the probabilistic method
Building complicated examples out of simple ones
Building examples with given properties
Cardinality, measure and category
Creating real numbers using limiting arguments
Finding subsets front page
How to change "for all x there exists y" into "there exists y such that for all x"
Making one mathematical object out of another
Universal constructions
Useful examples and counterexamples
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Recent articles
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Geometric view of Hölder's inequality
Diagonal arguments
Finding an interval for rational numbers with a high denominator
Try to prove a stronger result
Use self-similarity to get a limit from an inferior or superior limit.
Prove a consequence first
Lower degree by increasing dimension (or vice-versa)
Numerical optimization
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