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Mathematica > Mathematics and Algorithms > Formula Manipulation > 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.

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

Test whether

is an element of the reals:

Express domain membership for an expression:

Enter using Esc elem Esc:

Test whether

is an element of the reals:

Express domain membership for an expression:

Enter using Esc elem Esc:

Test domain membership:

Make domain membership assumptions:

Test domain membership using assumptions:

Specify variable domains:

Specify assumptions on objects matching a pattern:

For a single variable, the negation of Element is automatically converted to NotElement:

For multiple variables, the negation of Element is not automatically simplified:

Use LogicalExpand to find the representation in terms of NotElement:

When domain membership cannot be decided the Element statement remains unevaluated: