How high must a mountain be to be technically considered a "mountain"?
According to our dictionary, a mountain is "a natural elevation of the earth's surface rising more or less abruptly to a summit, and attaining an altitude greater than that of a hill, usually greater than 2000 ft. (610 m)." Note that this does not necessarily mean altitude above sea level; some elevated geographical features, such as plateaus, may not be considered mountains despite their altitude. Likewise, "mountains" may rise thousand of feet from the ocean floor but never break above the surface.
—The Fact Monster