Consider the function with
Natural value expected of at 1, by looking at values near 1, is 3
and not 5 .
For example, the error
whenever the point x is close to 1 by distance . In other words, , .
In fact, if we want close to by a distance (error) at most (any positive real number), then ,
i.e., given any we can choose such that is close to 3 by distance whenever x is close to 1 by distance .
This motivates our next definition.
with 
at 1, by looking at values near 1, is 3 
. In other words, 
, 
.
close to 
by a distance (error) at most 
(any positive real number), then 
, 
we can choose 
such that 
. 
