NotElement

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`NotElement`

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NotElement[x,dom]

or x∉dom asserts that is not an element of the domain dom.

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NotElement[x₁|…|x_n,dom]

asserts that none of the are elements of dom.

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NotElement[patt,dom]

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

Details

x∉dom can be entered as !el dom or x∖[NotElement]dom.
NotElement[x,dom] is equivalent to Not[Element[x, dom]].
NotElement[x₁|…|x_n,dom] is equivalent to Not[Element[x₁,dom]]&&…&&Not[Element[x_n,dom]].

Examples

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Basic Examples (3)Summary of the most common use cases

Test whether is not an element of the integers:

In[1]:=1

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https://wolfram.com/xid/0e7qpxf2-bf

Out[1]=1

Express that is not real:

In[1]:=1

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https://wolfram.com/xid/0e7qpxf2-dxbtxo

Out[1]=1

Enter using !elem:

In[1]:=1

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https://wolfram.com/xid/0e7qpxf2-cyw7h8

Out[1]=1

Scope (1)Survey of the scope of standard use cases

Test domain membership:

In[1]:=1

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https://wolfram.com/xid/0e7qpxf2-j0byqx

Out[1]=1

Properties & Relations (1)Properties of the function, and connections to other functions

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

In[1]:=1

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https://wolfram.com/xid/0e7qpxf2-e0mypk

Out[1]=1

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

In[2]:=2

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https://wolfram.com/xid/0e7qpxf2-ec5n8q

Out[2]=2

Use LogicalExpand to find the representation in terms of Element:

In[3]:=3

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https://wolfram.com/xid/0e7qpxf2-bg1b8r

Out[3]=3

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