You can use the function Element
to say e.g. $x,y,z\in\mathbb{R}$ via Element[x | y | z, Reals]
.
Now if I have a list of elements and want to say that they are all real I could do:
list = Array[x @ # &, 8]
Element[#, Reals]& /@ list /. List -> And
However, that seems unnecessarily complicated. Is there an easier way? Easier meaning shorter but also clear and easy to understand.
/.List->And
you can justApply
And
:And@@(Element[ #, Reals ]& /@ list)
. $\endgroup$Assuming[{x, y} ∈ Reals, (* stuff *)]
work, FYI. $\endgroup$|
or{x, y, z} \[Element] Ball[]
$\endgroup$Element[#, Reals] & /@ list
should be enough. $\endgroup$FullForm
of{x, y} ∈ Reals
is(x | y) ∈ Reals
, solist ∈ Reals
is by far the "nicest and cleanest" way to write your assertion. $\endgroup$