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What is a degree of freedom?

What is a degree of freedom? Here are some definitions.

Noun
  1. (physics) Any of the coordinates, a minimum number of which are needed to specify the motion of a mechanical system.
  2. (physics) Any of the independent variables required to specify the thermodynamic state of a system containing components and phases.
  3. (mathematics) Any unrestricted variable in a frequency distribution.
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