Rusting is a chemical reaction, so a chemical change of the original matter.
When Iron (symbol Fe) comes in contact with oxygen (symbol O), the result is a compound called Iron Oxide or rust. Iron Oxide or rust is found all over; both iron and oxygen form compounds quite easily, so they are not readily found alone. (The oxygen you breathe is O2, not elemental oxygen.)
Rust can come in different forms, because iron normally gives up 2 or 3 electrons when it forms compounds. We call these "oxidation states." When iron gives up 2 electrons, it gets a +2 charge, and when it gives up 3 electrons, it gets a +3 charge. To make a neutral compound it must then bond with some element in the proper ratio so as to remove its "excess" positive charge (or, replace its deficit negative charge.)
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