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\Re ^\infty = \left\{ {\xi \in \Re ^N \left| {\exists n \in N:\forall k > n\,\xi _k = 0} \right.} \right\}

\]

[/tex], N denoting the natural numbers?

If not, is there another symbol for the left hand side of the equation?

Is this also used with any other set containing a zero element?