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Useful inequalities cheat sheet

This is a collection of some of the most important mathematical inequalities. I tried to include non-trivial inequalities that can be useful in solving problems or proving theorems. I omitted many details, in some cases even necessary conditions (hopefully only when they were obvious). If you are not sure whether an inequality can be applied in some context, try to find a more detailed source for the exact definition. For lack of space I omitted proofs and discussions on when equality holds.

I didn't include inequalities which require lengthy definitions, inequalities involving complex functions, number theory, inequalities that rely on advanced calculus (most integral inequalities) and I also omitted inequalities with a pure geometric character. Many of the inequalities are special cases of others, but I tried to resist the temptation of including only the most general form (which may not be the most easily applicable).


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