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RealValuedNumericQ
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RealValuedNumericQ

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gives True if expr is a real-valued numeric quantity, and False otherwise.

Details

Examples

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Basic Examples  (2)Summary of the most common use cases

RealValuedNumericQ tests whether an object is a real-valued numeric quantity:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-jow3ul
Out[1]=1

RealValuedNumericQ[expr] gives True whenever N[expr] yields a number with head Real:

In[2]:=2
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https://wolfram.com/xid/0cps1p6cvysqwz-lmj1il
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0cps1p6cvysqwz-l7m3i7
Out[3]=3

A general symbolic expression is not a real-valued numeric quantity:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-wdffbp
Out[1]=1

Scope  (9)Survey of the scope of standard use cases

Integers and rationals are real-valued numeric quantities:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-yjfqow
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cps1p6cvysqwz-vg6efa
Out[2]=2

Approximate reals are real-valued numeric quantities:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-s9qsli
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cps1p6cvysqwz-s530m
Out[2]=2

RealValuedNumericQ gives True for real-valued mathematical constants:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-dqawgg
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cps1p6cvysqwz-r2bte
Out[2]=2

RealValuedNumericQ gives True for exact expressions representing real values:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-3qc2tf
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cps1p6cvysqwz-5lnsqz
Out[2]=2

Complex numbers are not real-valued quantities:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-0vmaxl
Out[1]=1

Exact complex quantities whose imaginary part is zero are real valued:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-jbt6qr
Out[1]=1

The number has a real part of and an imaginary part of :

In[2]:=2
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https://wolfram.com/xid/0cps1p6cvysqwz-4yt4le
Out[2]=2

Approximate complex numbers are not considered real valued even if their imaginary part equals zero:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-sprodj
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cps1p6cvysqwz-4plx4b
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0cps1p6cvysqwz-2dq4iq
Out[3]=3

RealValuedNumericQ[Infinity] gives False:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-h33pgt
Out[1]=1

RealValuedNumericQ[Overflow[]] and RealValuedNumericQ[Underflow[]] give True:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-d32kih
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cps1p6cvysqwz-d0gko
Out[2]=2

They are both treated as Real:

In[3]:=3
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https://wolfram.com/xid/0cps1p6cvysqwz-hqoir5
Out[3]=3

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

If Head[N[x]] is Real, then RealValuedNumericQ[x] is True:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-eqnb88

It is possible for RealValuedNumericQ[x] to be True and for N[x] to have head Complex:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-ehhqln
Out[1]=1

This indicates that x has an imaginary part that is exactly zero:

In[2]:=2
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https://wolfram.com/xid/0cps1p6cvysqwz-sxum3u
Out[2]=2

If RealValuedNumberQ[x] is True, then RealValuedNumericQ[x] is also True:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-qj1zbn

Possible Issues  (2)Common pitfalls and unexpected behavior

Exact quantities whose imaginary parts vanish may not be identified by RealValuedNumericQ:

In[1]:=1
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https://wolfram.com/xid/0cps1p6cvysqwz-njkwey
Out[2]=2

If detecting such numbers is important, simplify the expression before testing it:

In[3]:=3
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https://wolfram.com/xid/0cps1p6cvysqwz-i6blxm
Out[3]=3

An exact number and its numerical approximation may give different results for RealValuedNumericQ:

In[1]:=1
✖
https://wolfram.com/xid/0cps1p6cvysqwz-l1grhz
Out[1]=1

It is not possible to determine if the number is real, as its imaginary part is only approximately zero:

In[2]:=2
✖
https://wolfram.com/xid/0cps1p6cvysqwz-4aewp9
Out[2]=2
Wolfram Research (2023), RealValuedNumericQ, Wolfram Language function, https://reference.wolfram.com/language/ref/RealValuedNumericQ.html.
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Wolfram Research (2023), RealValuedNumericQ, Wolfram Language function, https://reference.wolfram.com/language/ref/RealValuedNumericQ.html.

Text

Wolfram Research (2023), RealValuedNumericQ, Wolfram Language function, https://reference.wolfram.com/language/ref/RealValuedNumericQ.html.

✖
Wolfram Research (2023), RealValuedNumericQ, Wolfram Language function, https://reference.wolfram.com/language/ref/RealValuedNumericQ.html.

CMS

Wolfram Language. 2023. "RealValuedNumericQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RealValuedNumericQ.html.

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Wolfram Language. 2023. "RealValuedNumericQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RealValuedNumericQ.html.

APA

Wolfram Language. (2023). RealValuedNumericQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RealValuedNumericQ.html

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Wolfram Language. (2023). RealValuedNumericQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RealValuedNumericQ.html

BibTeX

@misc{reference.wolfram_2025_realvaluednumericq, author="Wolfram Research", title="{RealValuedNumericQ}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/RealValuedNumericQ.html}", note=[Accessed: 19-May-2025 ]}

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@misc{reference.wolfram_2025_realvaluednumericq, author="Wolfram Research", title="{RealValuedNumericQ}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/RealValuedNumericQ.html}", note=[Accessed: 19-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_realvaluednumericq, organization={Wolfram Research}, title={RealValuedNumericQ}, year={2023}, url={https://reference.wolfram.com/language/ref/RealValuedNumericQ.html}, note=[Accessed: 19-May-2025 ]}

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@online{reference.wolfram_2025_realvaluednumericq, organization={Wolfram Research}, title={RealValuedNumericQ}, year={2023}, url={https://reference.wolfram.com/language/ref/RealValuedNumericQ.html}, note=[Accessed: 19-May-2025 ]}