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Fungrim entry: def588

Symbol: Binomial (nk){n \choose k} Binomial coefficient
Domain Codomain
nZ0andkZ0n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0} (nk)Z0{n \choose k} \in \mathbb{Z}_{\ge 0}
nCandkZ0n \in \mathbb{C} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0} (nk)C{n \choose k} \in \mathbb{C}
Table data: (P,Q)\left(P, Q\right) such that (P)    (Q)\left(P\right) \implies \left(Q\right)
Definitions:
Fungrim symbol Notation Short description
Binomial(nk){n \choose k} Binomial coefficient
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("def588"),
    SymbolDefinition(Binomial, Binomial(n, k), "Binomial coefficient"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(And(Element(n, ZZGreaterEqual(0)), Element(k, ZZGreaterEqual(0))), Element(Binomial(n, k), ZZGreaterEqual(0))), Tuple(And(Element(n, CC), Element(k, ZZGreaterEqual(0))), Element(Binomial(n, k), CC)))))

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2019-10-05 13:11:19.856591 UTC