The properties of the outcome of a limit function or an infinite series are known to be, often, different to any finite part of that series or limit. Check the

The properties of the outcome of a limit function or an infinite series are known to be, often, different to any finite part of that series or limit. Check the SEP under "supertasks" http://plato.stanford.edu/entries/spacetime-supertasks/ http://plato.stanford.edu/entries/spacetime-supertasks/