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What is a degree?

What is a degree? Here are some definitions.

Noun
  1. (obsolete outside heraldry) A step on a set of stairs; the rung of a ladder. [from 13th c.]
  2. An individual step, or stage, in any process or scale of values. [from 13th c.]
  3. A stage of rank or privilege; social standing. [from 13th c.]
  4. (genealogy) A ‘step’ in genealogical descent. [from 14th c.]
  5. (now rare) One's relative state or experience; way, manner. [from 14th c.]
  6. The amount that an entity possesses a certain property; relative intensity, extent. [from 14th c.]
  7. A stage of proficiency or qualification in a course of study, now especially an award bestowed by a university or, in some countries, a college, as a certification of academic achievement. (In the United States, can include secondary schools.) [from 14th c.]
  8. (geometry) A unit of measurement of angle equal to 1/360 of a circle's circumference. [from 14th c.]
  9. (physics) A unit of measurement of temperature on any of several scales, such as Celsius or Fahrenheit. [from 18th c.]
  10. (mathematics) The sum of the exponents of a term; the order of a polynomial. [from 18th c.]
  11. (graph theory) The number of edges that a vertex takes part in; a valency.
  12. (logic) The number of logical connectives in a formula.
  13. (surveying) The curvature of a circular arc, expressed as the angle subtended by a fixed length of arc or chord.
  14. (geography) A unit of measurement of latitude and longitude which together identify a location on the Earth's surface.
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