If you only counted stable substances as "elements", an awful lot of things would have to get a different name. Uranium wouldn't be an element at all, because even U-238 (the most common isotope, more than 99% of the stuff found in nature, http://en.wikipedia.org/wiki/Isotopes_of_uranium) will be reduced by half in a few billion years.
You could set some time limit of half life, below which is considered "completely unstable" and doesn't count, but what purpose would such an arbitrary division serve?
Yes, you can slam particles together in any combination, but the special thing about elements is that, for at least a few microseconds, it didn't need any external force or containment to hold together. A few microseconds is a long time at the subatomic scale.
You could set some time limit of half life, below which is considered "completely unstable" and doesn't count, but what purpose would such an arbitrary division serve?
Yes, you can slam particles together in any combination, but the special thing about elements is that, for at least a few microseconds, it didn't need any external force or containment to hold together. A few microseconds is a long time at the subatomic scale.