Editing Limits (section)

===Description of mental tasks needed to overcome the bottleneck===
One of the central issues in the Decoding interview has been the notion of "approaching", often colloquially used in the context of limits (such as in "the sequence approaches the limit 42"). Used in the mathematical context of limits "approaching" has a very precise meaning, eventually defined via the concept of limit, which differs slightly, but significantly from its colloquial meaning. The mathematical notion of "approaching" does not rule out that distance increases intermittently, while in its colloquial usage "approaching" is usually associated with continuously getting closer. The mathematical definition of limits takes great pains to include the case of an intermittent increase in distance. 

Take the following two statements as examples: <blockquote>(1) Anna is approaching her 50th birthday.</blockquote><blockquote>(2) While square dancing Anna is approaching Ben.</blockquote>
Statement (1) does not allow the possibility that the (temporal) distance between Anna and her Birthday increases. While Statement (2) does allow for the possibility that the distance between Anna and Ben increases temporarily, the mental image of most readers presumably excludes this possibility.