Using $Assumptions to define the domain of variable is straightforward, i.e. $Assumptions = Element[x, Reals]. Nevertheless, it's not clear how to test this assumption and return a True, False answer. The documentation seems to indicate that the statement Element[x, Reals] will return True if x is already defined as a member of Reals but I don't seem to be able to get this output consistently. Is there another way to test the domain assumptions of a variable?

  • 3
    $\begingroup$ $Assumptions=Element[x,Reals]; Simplify[Element[x,Reals]] returns True $\endgroup$
    – Bill
    Aug 24, 2021 at 15:47
  • $\begingroup$ $Assumptions only affect functions that use the option Assumptions. Simplify is typical: its default options include Assumptions :> $Assumptions $\endgroup$
    – Bob Hanlon
    Jul 14, 2022 at 16:55


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