Difference between revisions of "Uniqueness theorem for limits"
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Latest revision as of 20:51, 20 October 2011
Statement
Twosided limit
Suppose is a function and is a point such that is defined on both the immediate left and the immediate right of . The uniqueness theorem for limits states that if the limit of exists at (in the sense of existence as a finite real number) then it is unique. In other words:
If and , then .
Left hand limit
Suppose is a function and is a point such that is defined on the immediate left of . The uniqueness theorem for left hand limits states that if the left hand limit of exists at (in the sense of existence as a finite real number) then it is unique. In other words:
If and , then .
Right hand limit
Suppose is a function and is a point such that is defined on the immediate right of . The uniqueness theorem for right hand limits states that if the right hand limit of exists at (in the sense of existence as a finite real number) then it is unique. In other words:
If and , then .