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In classical Chinese mythology, it's typically Fire, Water, Earth, Wood (which includes control over plants as well as the wind), and Metal. In Greek (and by extension most European), Hindu, and Buddhist mythology, it's usually Fire, Air, Water, and Earth-with Aether (which can be "souls", "heart", "spirits", or Pure Energy) occasionally mixed in. Just what the "classical elements" are varies from culture to culture. May involve the capability to summon Elementals, the living embodiment of the elements themselves.
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It also makes for easy Super-Hero Speciation. A character with elemental power in animation will often have the fitting eye color. These "elements" are probably the source of the association of colors with personality traits. This usually goes hand in hand with Personality Powers-you're not likely to find a calm and collected guy who can shoot fire, for instance. The most common use is to give characters some superpower over an aspect of nature-like a character who can conjure or control fire or water, given the right conditions. Alternately, fire corresponds to energy, particularly the heat energy that moves matter from one state to another).
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The discovery of the atom mostly disproved that, but the idea was so deeply rooted in mankind's mind, that it's still used in nearly every supernatural fictional setting (note that the classical elements actually correspond to a different scientific concept: the phases of matter, provided you count plasma as a fourth phase & not just as a subset of gas. Thus, all of the world was made up of natural forces such as "earth, air, fire, water" et al. In the past, it was thought that all of matter could be classified into easily viewable "elements" that one can observe with the naked eye.
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