1. An improved electrically operated, directly overwritable, single-cell memory element comprising: a pair of spacedly disposed contacts, said contacts providing terminals for reading information stored in and writing information to said memory element; a volume of memory material defining a single cell memory element disposed between said contacts, said memory material constituting means for assuming a large dynamic range of electrical resistance values with the ability to be set directly to one of a plurality of resistance values within said dynamic range without the need to be set to a specific starting or erased resistance value, regardless of the previous resistance value of said material in response to a selected electrical input signal; said volume of memory material formed from a plurality of constituent atomic elements each of which is present throughout the entire volume of memory material; and said volume of memory material including compositional means adapted to substantially stabilize the resistance of said volume of memory material at a selected resistance value and said volume of memory material adapted to remain set at said selected resistance value without drift after the input signal has been terminated.