Squeeze theorem

"Sandwich theorem" redirects here. For the result in measure theory, see Ham sandwich theorem. For Sandwich theory (physics), see Sandwich theory.
Illustration of the squeeze theorem
When a sequence lies between two other converging sequences with the same limit, it also converges to this limit.

In calculus, the squeeze theorem (also known as the sandwich theorem, among other names[a]) is a theorem regarding the limit of a function that is bounded between two other functions.

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