Symbol:

`Minimum`— $\mathop{\min}\limits_{P\left(x\right)} f\!\left(x\right)$ — Minimum value of a set or functionThis operator can be called with 1 or 3 arguments.

Called with 1 argument,

`Minimum(S)`, rendered $\min\left(S\right)$, represents the minimum element of the set $S$. This operator is only defined if $S$ is a subset of $\mathbb{R} \cup \left\{-\infty, +\infty\right\}$ and the minimum exists.Called with 3 arguments,

`Minimum(f(x), x, P(x))`, rendered $\mathop{\min}\limits_{P\left(x\right)} f\!\left(x\right)$, represents $\min\left(\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}\right)$.The argument

`x`to this operator defines a locally bound variable. The corresponding predicate $P\!\left(x\right)$ must define the domain of $x$ unambiguously; that is, it must include a statement such as $x \in S$ where $S$ is a known set. More generally,`x`can be a collection of variables $\left(x, y, \ldots\right)$ all of which become locally bound, with a corresponding predicate $P\!\left(x, y, \ldots\right)$.Definitions:

Fungrim symbol | Notation | Short description |
---|---|---|

Minimum | $\mathop{\min}\limits_{P\left(x\right)} f\!\left(x\right)$ | Minimum value of a set or function |

RR | $\mathbb{R}$ | Real numbers |

Infinity | $\infty$ | Positive infinity |

SetBuilder | $\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$ | Set comprehension |

Source code for this entry:

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