Normal sequence

In mathematics, the term normal sequence has multiple meanings, depending on the area of specialty.  In general, it is a sequence with "nice" properties.

 In set theory, a normal sequence is one that is continuous and strictly increasing.
 In probability theory, normal sequence may be used synonymously with normal number.

References 
 Thomas Jech.  Set Theory, 3rd millennium ed., 2002, Springer Monographs in Mathematics,Springer,