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Proving "for all" statements
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Prove the result for some cases and deduce it for the rest
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Prove the result on a delta-net first
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[QUICK DESCRIPTION] In probabilistic arguments, one sometimes wants to prove that it is possible for a statement to be true for every element of an infinite set, and one knows that for each element of the set a slightly stronger statement is true with probability at least $1-\epsilon$ for some very small $\epsilon$. If there is a natural metric on the set, one can sometimes achieve this by proving that the set contains a $\delta$-net of size $N<\epsilon^{-1}$, and also that if the stronger result holds for every element of a $\delta$-net, then the weaker result holds everywhere. Techniques for proving the existence of small $\delta$-nets can be found in the article [[Finding small nets]]. [note article incomplete] This article has yet to be written. [/note]
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