RealAbs

RealAbs[x]

gives the absolute value of the real number x.

Details

• RealAbs is also known as modulus.
• Mathematical function, suitable for both symbolic and numerical manipulation.
• RealAbs[x] is effectively equivalent to Piecewise[{{x,x>=0}},-x].
• RealAbs is continuous and differentiable everywhere except at the origin.
• RealAbs[x] is left unevaluated if x is not a numeric quantity.
• RealAbs can be used with Interval and CenteredInterval objects. »
• RealAbs automatically threads over lists.

Examples

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Basic Examples(4)

Positive numbers:

Negative numbers:

Plot RealAbs over a subset of the reals:

Derivative of RealAbs:

Indefinite integral:

Scope(29)

Numerical Evaluation(6)

Evaluate numerically:

RealAbs remains unevaluated for imaginary numbers:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate efficiently at high precision:

RealAbs threads elementwise over lists and matrices:

RealAbs can be used with Interval and CenteredInterval objects:

Specific Values(5)

Values of RealAbs at particular points:

Value at zero:

Values at infinity:

Evaluate symbolically:

Find values of for which :

Substitute in the value of to create pairs:

Visualize the result:

Visualization(3)

Plot :

Plot RealAbs along with its first derivative:

Plot RealAbs in three dimensions:

Function Properties(10)

RealAbs is defined only for real inputs:

The range of RealAbs is the non-negative reals:

RealAbs is an even function:

RealAbs is not an analytic function:

It has a singularity at the origin but no discontinuities:

RealAbs is neither nondecreasing nor nonincreasing:

RealAbs is not injective:

RealAbs is not surjective:

RealAbs is non-negative:

RealAbs is convex:

Differentiation and Integration(5)

First derivative:

Obtain an equivalent expression using the definition of derivative:

The function Abs of complex variables is not differentiable:

Higher derivatives:

Compute the indefinite integral using Integrate:

Verify the antiderivative:

Definite integral:

More integrals:

Applications(7)

Color plots according to RealAbs:

Solve a differential equation with RealAbs:

Compute the Fourier cosine series of RealAbs:

Compute a series involving RealAbs:

Solve an equation involving RealAbs:

Prove an inequality containing RealAbs:

Simplify expressions containing RealAbs:

Properties & Relations(8)

RealAbs is defined only for real numbers:

Abs is defined for complex numbers:

RealAbs is a differentiable function:

Abs is not differentiable:

RealAbs is an integrable function:

Abs is integrable only for real arguments:

RealAbs is idempotent:

Definite integration:

Integral transforms:

Convert into Piecewise:

Denest:

Neat Examples(1)

Form nested functions involving RealAbs:

Wolfram Research (2017), RealAbs, Wolfram Language function, https://reference.wolfram.com/language/ref/RealAbs.html (updated 2021).

Text

Wolfram Research (2017), RealAbs, Wolfram Language function, https://reference.wolfram.com/language/ref/RealAbs.html (updated 2021).

CMS

Wolfram Language. 2017. "RealAbs." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/RealAbs.html.

APA

Wolfram Language. (2017). RealAbs. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RealAbs.html

BibTeX

@misc{reference.wolfram_2024_realabs, author="Wolfram Research", title="{RealAbs}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/RealAbs.html}", note=[Accessed: 19-July-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_realabs, organization={Wolfram Research}, title={RealAbs}, year={2021}, url={https://reference.wolfram.com/language/ref/RealAbs.html}, note=[Accessed: 19-July-2024 ]}