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Fungrim entry: 25b7bd

n!>Cnn ! > {C}^{n}
Assumptions:n∈Z≥1  and⁡  C∈(0,∞)  and⁡  n≥Cen \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; C \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; n \ge C e
TeX:
n ! > {C}^{n}

n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; C \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; n \ge C e
Definitions:
Fungrim symbol Notation Short description
Factorialn!n ! Factorial
Powab{a}^{b} Power
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity∞\infty Positive infinity
ConstEee The constant e (2.718...)
Source code for this entry:
Entry(ID("25b7bd"),
    Formula(Greater(Factorial(n), Pow(C, n))),
    Variables(C, n),
    Assumptions(And(Element(n, ZZGreaterEqual(1)), Element(C, OpenInterval(0, Infinity)), GreaterEqual(n, Mul(C, ConstE)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC