For example, integers are an ADT, defined as the values ..., −2, −1, 0, 1, 2, ..., and by the operations of addition, subtraction, multiplication, and division, together with greater than, less than, etc., which behave according to familiar mathematics (with care for integer division), independently of how the integers are represented by the computer. [lower-alpha 1] Explicitly, "behavior" includes obeying various axioms (associativity and commutativity of addition, etc.), and preconditions on operations (cannot divide by zero). Typically integers are represented in a data structure as binary numbers, most often as two's complement, but might be binary-coded decimal or in ones' complement, but the user is abstracted from the concrete choice of representation, and can simply use the data as data types.