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Fungrim entry: fa3b53

(nk)≤2n{n \choose k} \le {2}^{n}
Assumptions:n∈Z≥0 and⁡ k∈Z≥0n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0}
TeX:
{n \choose k} \le {2}^{n}

n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Binomial(nk){n \choose k} Binomial coefficient
Powab{a}^{b} Power
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("fa3b53"),
    Formula(LessEqual(Binomial(n, k), Pow(2, n))),
    Variables(n),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(k, ZZGreaterEqual(0)))))

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2019-06-18 07:49:59.356594 UTC