Definition 59 (Landau 43). For each bound ξ, the operation +ξ is the specific operation of adding ξ, and the operation −ξ is the specific operation of removing ξ. The operation that adds and removes the same bound is 0. These operations are the real numbers. +ξ is called positive and −ξ negative. −ξ and −η are the same when ξ and η are the same. Where it causes no confusion, ξ also denotes +ξ. Capital Greek letters Ξ, Θ, Λ, Φ stand for real numbers.
Landau says here: "We create a new number 0" and "we also create numbers ... which we will call negative numbers." Nothing is created here. These are derived numbers in the sense of Definition 3: specific operations, each defined by a bound.
In the order of derivation the whole ones come first. +n and −n need only number and addition, and they were the first derived numbers. Landau's order reaches signed numbers last, and so reaches them over bounds. The earlier ones are the case in which ξ is a whole bound (Definition 67 below).