prepositions - "defined by" or "defined as"?


MY main interest is in the mathematical context, where one defines objects by a formula. I can imagine 2 cases :



  1. Direct case, "direct definition": The function f is defined by/as f=a+b+c

  2. Implicit definition: The number x is defined by/as a = g(x)


I would tend to use as for the case 1 and by for the second one.




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