- We say that the function
has a right limit
at
and we denote
if

- We say that the function
has a left limit
at
and we denote
if

We define the ``integer part function'':

Let now . Then: and .

Therefore the integer part function has no limit at 0, by Proposition 1.2. Similar definitions can be written for infinite one-sided limits. Please try to do it.

For example, if , then and .

- has a left limit at ;
- has a right limit at ;
- .

For example, let . Then and . Hence, has no limit at 0 (see Figure 7).

Noah Dana-Picard 2007-12-28