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 .
For example, let . Then and . Hence, has no limit at 0 (see Figure 7).
Noah Dana-Picard 2007-12-28