First let's define the term oxidation number. It is a way of assigning charges to each atom of a chemical compound or species. In other words, if you pretended that each atom of a compound or species was an ion, the oxidation number for each element would be the charge assigned to that particular element as a part of the whole. For an ion with a single element, the oxidation number of the element is the charge of the ion. For a neutral chemical compound, the oxidation numbers of the individual atoms must add up to a total of zero. O2 is molecular oxygen and is composed of two oxygen atoms bonded together with a double bond. Since it has no overall charge and is composed of a single type of element, both of the oxygen atoms in O2 must have an oxidation number of 0 since they both have to be the same and add up to 0. Now, 1/2 O2 is another way of saying just plain O, and the same rules apply here. O has a total charge of zero and therefore the oxidation number of O would have to be zero as well.