DOCUMENTATION CENTER SEARCH

Mathematica > Assumptions and Domains >

Element ()

Element[x, dom]
or x

dom asserts that x is an element of the domain dom.

Element[{x₁, x₂, ...}, dom]
asserts that all the x_i are elements of dom.

Element[patt, dom]
asserts that any expression matching the pattern patt is an element of dom.

MORE INFORMATION

xdom can be entered as x Esc el Esc dom or x\[Element]dom.

Element can be used to set up assumptions in Simplify and related functions.

Possible domains are:

	Algebraics	algebraic numbers
	Booleans	True or False
	Complexes	complex numbers
	Integers	integers
	Primes	prime numbers
	Rationals	rational numbers
	Reals	real numbers

xdom if possible evaluates immediately when x is numeric.

(x₁|x₂|...)dom is equivalent to {x₁, x₂, ...}dom.

{x₁, x₂, ...}dom evaluates to (x₁|x₂|...)dom if its truth or falsity cannot immediately be determined.

Basic Examples (3)

Test whether

is an element of the reals:

Express domain membership for an expression:

Enter using Esc elem Esc:

Properties & Relations (1)

Possible Issues (1)

Simplify MemberQ IntegerQ Assumptions Condition PatternTest Equal Less Divisible CoprimeQ Booleans Primes Exists ForAll

Simplifying with Assumptions

Using Assumptions

Assumptions and Domains

Formula Manipulation

Number Recognition

Number Theory

NKS|Online (A New Kind of Science)

New in 4 | Last modified in 5

© 2008 Wolfram Research, Inc.

Ask a question about this page | Suggest an improvement | Leave a message for the team