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Min

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Min[x1, x2, ...]
    yields the numerically smallest of the xi.
Min[{x1, x2, ...}, {y1, ...}, ...]
    yields the smallest element of any of the lists.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= MinMax[<|"a" -> 3, "b" -> 1, "c" -> 9|>]
Out[1]= {1, 9}

Implementation notes

Algorithm. builtin_min mirrors Max: it flattens List arguments, scans real-numeric atoms for the minimum (via expr_compare), collects distinct symbolic terms, and treats Infinity/-Infinity/Overflow[] as identity/absorbing elements. All-numeric input returns the single smallest value; mixed input returns Min[...] over the numeric minimum and the remaining symbolic terms, or NULL if nothing simplified. Empty Min[] is Infinity.

Attributes: Flat, NumericFunction, OneIdentity, Orderless, Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References

Notes & additional examples

Worked examples

In[1]:= Min[3, 7, 2]
Out[1]= 2

In[1]:= Min[1/3, 2/7, 5/11]
Out[1]= 2/7

In[1]:= Min[x, 0, Infinity]
Out[1]= Min[0, x]

In[1]:= Min[{}]
Out[1]= Infinity

Notes

Min[x1, x2, ...] returns the numerically smallest argument, and Min of several lists returns the smallest element across all of them. Comparisons are exact, so rationals are ordered without converting to floating point — Min[1/3, 2/7, 5/11] correctly picks 2/7. With symbolic arguments Min stays unevaluated but still prunes operands it can decide: Min[x, 0, Infinity] drops Infinity (which can never be a minimum) and returns Min[0, x]. The empty case Min[{}] returns Infinity, the identity element of minimisation — the value that leaves any subsequent Min unchanged.