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A non-trivial circular argument can often be usefully perturbed to a non-circular one
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Create an epsilon of room
A non-trivial circular argument can often be usefully perturbed to a non-circular one
I have a problem to solve in real analysis and I do not believe that a fundamental idea is needed
If an argument looks promising but needs a hypothesis, assume the hypothesis for now but try to remove it later
Interchange integrals or sums
Linearize the phase
Prove the result for some cases and deduce it for the rest
To make a function nicer without changing it much, convolve it with an approximate delta function
Use Fourier expansion to eliminate nasty cutoffs
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Try to prove a stronger result
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Prove a consequence first
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