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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