Documentation

Mathematica Teacher's Edition

Built-in Functions

Algebraic Computation

Formula Manipulation

Element

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 evaluates to ( | | ... ) dom if its truth or falsity cannot immediately be determined.
See The Mathematica Book on the web: Section 1.4.6 and Section 3.3.10.
See also: Simplify, MemberQ, IntegerQ, Condition, PatternTest, Equal, Less.

Further Examples