The squeeze theorem, also known as the squeezing theorem, pinching theorem, or sandwich theorem, states that if 
on a common domain sufficiently close to its accumulation
point 
, excluding 
itself, and
 |
then 
. In the above diagram the functions 
and 
bound 
from below and above, so 
.
For sequences, if 
for all sufficiently large 
and
 |
then 
. For any 
, both bounding sequences
eventually lie between 
and 
, so the middle sequence
does as well.
