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based on an earlier version of the Wolfram Language.
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Element

Element
or asserts that x is an element of the domain dom.
Element
asserts that all the are elements of dom.
Element
asserts that any expression matching the pattern patt is an element of dom.
  • can be entered as x Esc el Esc dom or .
  • Element can be used to set up assumptions in Simplify and related functions.
  • Possible domains are:
Algebraicsalgebraic numbers
BooleansTrue or False
Complexescomplex numbers
Integersintegers
Primesprime numbers
Rationalsrational numbers
Realsreal numbers
  • if possible evaluates immediately when x is numeric.
  • is equivalent to .
  • evaluates to 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:
In[1]:=
Click for copyable input
Out[1]=
 
Express domain membership for an expression:
In[1]:=
Click for copyable input
Out[1]=
 
Enter using Esc elem Esc:
In[1]:=
Click for copyable input
Out[1]=
Test domain membership:
Make domain membership assumptions:
Test domain membership using assumptions:
Specify variable domains:
Specify assumptions on objects matching a pattern:
TraditionalForm formatting:
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:
New in 4 | Last modified in 5