yields the numerically smallest of the xi.


yields the smallest element of any of the lists.


  • Min yields a definite result if all its arguments are real numbers.
  • In other cases, Min carries out some simplifications.
  • Min[] gives Infinity.
  • Min works on SparseArray objects.


open allclose all

Basic Examples  (3)

Minimum of two numbers:

Minimum of a list:

Plot over a subset of the reals:

Scope  (23)

Numerical Evaluation  (5)

Evaluate numerically:

Evaluate to high precision:

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

Evaluate efficiently at high precision:

The minimum of all elements of a matrix:

The minima of all rows:

The minima of all columns:

Min works with real-valued intervals:

Specific Values  (5)

Values of Min at fixed points:

Values at infinity:

Evaluate symbolically:

Solve equations and inequalities:

Find a value of x for which Min[{Sin[x],Cos[x]}]1/2:

Visualization  (3)

Plot the Min of several functions:

Plot Min in three dimensions:

Plot Min of three functions in three dimensions:

Function Properties  (5)

Min is only defined for real-valued inputs:

The range of Min is all real numbers:

Min effectively flattens out all lists:

Basic symbolic simplification is done automatically:

Additional simplification can be done using Simplify:

Differentiation and Integration  (5)

First derivative with respect to x:

Higher derivatives with respect to x:

Formula for the ^(th) derivative with respect to x:

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

Definite integrals:

Applications  (4)

Use in bounds of iterator variables:

Cumulative minima:

Find the lowest point of a plotted curve:

Mean of the length ratio of a randomly broken stick:

Rfunction-based solid modeling:

Properties & Relations  (6)

With no arguments, Min returns Infinity:

Min is Flat and Orderless:

Use PiecewiseExpand to express Min and Max as explicit cases:

Use FullSimplify to simplify Min expressions:

Minimize a function containing Min:

Min can be differentiated:

Possible Issues  (2)

Min flattens lists, rather than being Listable:

Oneargument form evaluates for any argument:

Neat Examples  (2)

Two-dimensional sublevel sets:

Three-dimensional sublevel sets:

Wolfram Research (1988), Min, Wolfram Language function, https://reference.wolfram.com/language/ref/Min.html (updated 2003).


Wolfram Research (1988), Min, Wolfram Language function, https://reference.wolfram.com/language/ref/Min.html (updated 2003).


@misc{reference.wolfram_2021_min, author="Wolfram Research", title="{Min}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/Min.html}", note=[Accessed: 05-December-2021 ]}


@online{reference.wolfram_2021_min, organization={Wolfram Research}, title={Min}, year={2003}, url={https://reference.wolfram.com/language/ref/Min.html}, note=[Accessed: 05-December-2021 ]}


Wolfram Language. 1988. "Min." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2003. https://reference.wolfram.com/language/ref/Min.html.


Wolfram Language. (1988). Min. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Min.html