Cl 的oxidation number 不是fix?

Which textbook states that the oxidation number of is fixed at +1? It is a great mistake.

Actually, the oxidation number of Cl compounds is variable, but not fixed. Also, the commonest oxidation number of Cl is -1, but not +1.

Common oxidation numbers of Cl is :
Oxidation number -1: e.g. in HCl, NaCl, Cl-
Oxidation number 0: in Cl2
Oxidation number +1: e.g. in HOCl, KOCl, OCl-
Oxidation number +3: e.g. in HClO2, KClO2, ClO2-
Oxidation number +5: e.g. in HClO3, KClO3, ClO3-
Oxidation number +7: e.g. in HClO4, KClO4, ClO4-

There is a tendency for Cl to have an oxidation number of -1, because when it is an ion, it carries a 1- charge. However, oxidation number CAN'T be fixed for any species, this is because if it is fixed, then there will not be any reaction happening, since redox reaction relies upon the fact that the oxidation number of species in a molecule changes. So for example, when Fe3+ is changed into Fe2+, this is a reduction reaction, because the oxidation number of Fe has decreased from +3 to +2 (also the fact that a reduction is a gain of electrons). So in your example, Cl in KClO3 is in +5. However, there are examples when it is +1, like when it is in Sodium (I) Chlorate, NaOCl, or when it is in -1, like in Sodium Chloride, or 0, in chlorine molecules, Cl2. There are disproportionation reactions for Cl2 which means that Cl2 is simultaneously oxidised and reduced in the same reaction.

Cl2 + H2O --> HOCl + HCl (from 0 to +1 and -1) (at room temperature)
3Cl2 + NaOH --> NaOCl3 + HCl ( from 0 to +5 and -1) (at 75C +)