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Just-do-it proofs
Building examples with given properties
Existence proofs
Finding subsets front page
Greedy algorithms
How to use the continuum hypothesis
If you are getting stuck, then try to prove rigorously that your approach cannot work
To construct exotic sets, use limiting arguments
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Littlewood-Paley heuristic for derivative
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
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