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squeeze theorem

n. (context lang=en math) A theorem used to confirm the limit of a function via comparison with two other functions whose limits are known or easily computed.

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Squeeze theorem

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In calculus, the squeeze theorem known also as the pinching theorem, the sandwich theorem, the sandwich rule, and sometimes the squeeze lemma is a theorem regarding the limit of a function.

The squeeze theorem is used in calculus and mathematical analysis. It is typically used to confirm the limit of a function via comparison with two other functions whose limits are known or easily computed. It was first used geometrically by the mathematicians Archimedes and Eudoxus in an effort to compute , and was formulated in modern terms by Gauss.

In many languages (e.g. French, German, Italian and Russian), the squeeze theorem is also known as the two policemen (and a drunk) theorem, or some variation thereof. The story is that if two policemen are escorting a drunk prisoner between them, and both officers go to a cell, then (regardless of the path taken, and the fact that the prisoner may be wobbling about between the policemen) the prisoner must also end up in the cell.