Theorem 3.1 is mainly use to disprove the existence of a limit at some point, as shown in the next example.
. This function has no limit at 0:
As the limit of a function is unique ( v.s. Prop. 1.2
it cannot be equal both to 0 and to 1, therefore
has no limit at 0 (in Figure 8
we show two drawings of the graph of
, zooming to show how ``messy'' looks the graph for
close to 0).