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limit from the left and right


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The statement that f(x) tends to l as x tends to a from the left can be written: f(x)→ l as xa−. Another way of writing this is

The formal definition says that this is so if, given ε>0, there is a number δ>0 such that, for all x strictly between aδ and a, f(x) lies between lε and l+ε. In place of xa−, some authors use xa. In the same way, the statement that f(x) tends to l as x tends to a from the right can be written: f(x) → l as xa+. Another way of writing this isThe formal definition says that this is so if, given ε>0, there is a number δ>0 such that, for all x strictly between a and a+δ, f(x) lies between lε and l+ε. In place of xa+, some authors use xa. For example, if f(x)=x−[x], then

Subjects: Mathematics.


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