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Strengthen your inductive hypothesis
If your topological invariant takes integer values, they may well be homology classes in disguise
Induction front page
Simplify your problem by generalizing it
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Littlewood-Paley heuristic for derivative
Littlewood-Paley heuristic
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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