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Mathematica > Mathematics and Algorithms > Formula Manipulation > Assumptions and Domains >

Built-in Mathematica Symbol

NotElement ()

NotElement[x, dom]
or x

dom asserts that

is not an element of the domain dom.

NotElement[x₁|...|x_n, dom]
asserts that none of the

are elements of dom.

NotElement[patt, dom]
asserts that any expression matching the pattern patt is not an element of the domain dom.

NotElement[x₁|...|x_n, dom] is equivalent to Not[Element[x₁, dom]]&&...&&Not[Element[x_n, dom]].

Test whether

is not an element of the integers:

Express that

is not real:

Enter using Esc !elem Esc:

Test whether

is not an element of the integers:

Express that

is not real:

Enter using Esc !elem Esc:

Test domain membership:

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

For multiple variables the negation of NotElement is not automatically simplified:

Use LogicalExpand to find the representation in terms of Element: