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Approximation front page
C
Clarify your problem by making it more abstract
I
If an argument looks promising but needs a hypothesis, assume the hypothesis for now but try to remove it later
If you don't know how to make a decision, then don't make it
L
Look at small cases
S
Simplify your problem by generalizing it
Strengthen your inductive hypothesis
T
Think axiomatically even about concrete objects
To understand an object, consider treating it as one of a family of objects and analysing the family
Try to prove a stronger result
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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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