Fluorine is a halogen and is highly electronegative, with an oxidation state of always
1 in its compounds. This lack of variability in oxidation states distinguishes it from other halogens, such as chlorine, bromine, and iodine, which can exhibit a range of oxidation states. For example, chlorine can show oxidation states of
1, +1, +3, +5, and +7.
Final Answer: The element not showing variable oxidation states is fluorine.