A mathematical object is uniquely determined by a set of conditions if only one object with those conditions can exist. Example: A line is uniquely determined by two points. Given those two points, only one line can exist that passes through those points.
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McAdams, David E. Uniquely Determined. 5/5/2011. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/u/uniquelydetermined.html.
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