Element[x, dom] or asserts that x is an element of the domain dom.
Element[, , ... , dom] asserts that all the are elements of dom.
Element[patt, dom] asserts that any expression matching the pattern patt is an element of dom.
can be entered as x elem dom or x \[Element] dom.
Element can be used to set up assumptions in Simplify and related functions.
Possible domains are:
if possible evaluates immediately when x is numeric.
Examples: Pi Algebraics ; Pi Reals .
( | | ... ) dom is equivalent to , , ... dom.
, , ... dom evaluates to ( | | ... ) dom if its truth or falsity cannot immediately be determined.
See The Mathematica Book: Section 1.4.6 and Section 3.3.10.
See also: Simplify, MemberQ, IntegerQ, Assumptions, Condition, PatternTest, Equal, Less, NotElement.