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Turn sets into functions
Decompose your ring using idempotents
Extremal combinatorics front page
If you are getting stuck, then try to prove rigorously that your approach cannot work
If your problem can be expressed in terms of convolutions and inner products then take the Fourier transform
What can a lower bound say about potential proofs of the upper bound?
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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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