Follows from the Sandwich Theorem for sequences.

Next we look at another way of describing the statement that a function has a limit at point. To predict the value of
a function at a point we have to analyze the values of the function as approaches . In our
definition above, we used the concept of sequences  . One can directly use the notion of distance for
this. Suppose we want to analyse whether a number  is the natural value expected of  at or not?
At a point near , is the error one will be making for being not equal to value expected. If
 is the value expected, then one would like to make this error small, smaller than any given value. Let us say that
this error is less than a given value for all points sufficiently close to . Let us look at an example.