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Reals
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Reals

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represents the domain of real numbers, as in x∈Reals.

Details

  • x∈Reals evaluates immediately if x is a numeric quantity.
  • Simplify[expr∈Reals,assum] can be used to try to determine whether an expression corresponds to a real number under the given assumptions.
  • (x1|x2|…)∈Reals and {x1,x2,…}∈Reals test whether all xi are real numbers.
  • Within Simplify and similar functions, objects that satisfy inequalities are always assumed to be real.
  • Reals is output in StandardForm or TraditionalForm as TemplateBox[{}, Reals]. This typeset form can be input using reals.

Examples

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

is a real number:

In[1]:=1
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https://wolfram.com/xid/0mrem5-bur9kd
Out[1]=1

If is a real number, so is :

In[1]:=1
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https://wolfram.com/xid/0mrem5-b4frm7
Out[1]=1

Find real solutions of an equation:

In[1]:=1
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https://wolfram.com/xid/0mrem5-eqszwi
Out[1]=1

Scope  (5)Survey of the scope of standard use cases

Test domain membership of a numeric expression:

In[1]:=1
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https://wolfram.com/xid/0mrem5-crra11
Out[1]=1

Make domain membership assumptions:

In[1]:=1
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https://wolfram.com/xid/0mrem5-cn7igo
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0mrem5-duaa4b
Out[2]=2

Specify the default domain over which a function should work:

In[1]:=1
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https://wolfram.com/xid/0mrem5-g9ic3l
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0mrem5-muk485
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0mrem5-bfezed
Out[3]=3

Test whether several numbers are real numbers:

In[1]:=1
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https://wolfram.com/xid/0mrem5-3pjyzh
Out[1]=1

If any number is explicitly non-real, the result is False:

In[2]:=2
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https://wolfram.com/xid/0mrem5-m7ag79
Out[2]=2

TraditionalForm formatting:

In[1]:=1
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https://wolfram.com/xid/0mrem5-4xdcq9

Properties & Relations  (3)Properties of the function, and connections to other functions

Reals contains Rationals, Integers, and Primes:

In[1]:=1
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https://wolfram.com/xid/0mrem5-culh0e
Out[1]=1

Reals is contained in Complexes:

In[1]:=1
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https://wolfram.com/xid/0mrem5-ciam4c
Out[1]=1

Reals neither contains nor is contained in Algebraics:

In[1]:=1
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https://wolfram.com/xid/0mrem5-k8venp
Out[1]=1
Wolfram Research (1999), Reals, Wolfram Language function, https://reference.wolfram.com/language/ref/Reals.html (updated 2017).
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Wolfram Research (1999), Reals, Wolfram Language function, https://reference.wolfram.com/language/ref/Reals.html (updated 2017).

Text

Wolfram Research (1999), Reals, Wolfram Language function, https://reference.wolfram.com/language/ref/Reals.html (updated 2017).

✖
Wolfram Research (1999), Reals, Wolfram Language function, https://reference.wolfram.com/language/ref/Reals.html (updated 2017).

CMS

Wolfram Language. 1999. "Reals." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Reals.html.

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Wolfram Language. 1999. "Reals." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Reals.html.

APA

Wolfram Language. (1999). Reals. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Reals.html

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Wolfram Language. (1999). Reals. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Reals.html

BibTeX

@misc{reference.wolfram_2025_reals, author="Wolfram Research", title="{Reals}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/Reals.html}", note=[Accessed: 25-March-2025 ]}

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@misc{reference.wolfram_2025_reals, author="Wolfram Research", title="{Reals}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/Reals.html}", note=[Accessed: 25-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_reals, organization={Wolfram Research}, title={Reals}, year={2017}, url={https://reference.wolfram.com/language/ref/Reals.html}, note=[Accessed: 25-March-2025 ]}

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@online{reference.wolfram_2025_reals, organization={Wolfram Research}, title={Reals}, year={2017}, url={https://reference.wolfram.com/language/ref/Reals.html}, note=[Accessed: 25-March-2025 ]}