With all these definitions, it is convenient to include 0 (corresponding to the empty set) as a natural number. Including 0 is now the common convention among set theorists[22] and logicians.[23] Other mathematicians also include 0,[lower-alpha 1] and computer languages often start from zero when enumerating items like loop counters and string- or array-elements.[24][25] On the other hand, many mathematicians have kept the older tradition to take 1 to be the first natural number.[26]