Symbol:

`Solutions`— $\mathop{\operatorname{solutions}\,}\limits_{P\left(x\right)} Q\!\left(x\right)$ — Solution set`Solutions(Q(x), x, P(x))`, rendered $\mathop{\operatorname{solutions}\,}\limits_{P\left(x\right)} Q\!\left(x\right)$, represents the set of values $x$ satisfying $P\!\left(x\right)$ and $Q\!\left(x\right)$.

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 |
---|---|---|

Solutions | $\mathop{\operatorname{solutions}\,}\limits_{P\left(x\right)} Q\!\left(x\right)$ | Solution set |

Source code for this entry:

Entry(ID("5862bb"), SymbolDefinition(Solutions, Solutions(Q(x), x, P(x)), "Solution set"), Description(SourceForm(Solutions(Q(x), x, P(x))), ", rendered", Solutions(Q(x), x, P(x)), ", represents the set of values", x, "satisfying", P(x), "and", Q(x), "."), Description("The argument", SourceForm(x), "to this operator defines a locally bound variable.", "The corresponding predicate", P(x), "must define the domain of", x, "unambiguously; that is, it must include a statement such as", Element(x, S), "where", S, "is a known set.", "More generally,", SourceForm(x), "can be a collection of variables", Tuple(x, y, Ellipsis), "all of which become locally bound, with a corresponding predicate", P(x, y, Ellipsis), "."))