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Completeness (mathematics)
From Citizendium, the Citizens' Compendium
In mathematics, completeness is a property ascribed to a metric space in which every Cauchy sequence in that space is convergent. In other words, every Cauchy sequence in the metric space tends in the limit to a point which is again an element of that space. Hence the metric space is, in a sense, "complete."
Formal definition
Let X be a metric space with metric d. Then X is complete if for every Cauchy sequence 
there is an associated element 
such that 
.
