query: Which has a higher order of growth, n! or n^n?
positive_passages.docid: 12914
positive_passages.text: What's the limit of the sequence $\lim\limits_{n \to\infty} \frac{n!}{n^n}$?
negative_passages.docid: 71432
negative_passages.text: What does the expression $1^n$ mean as a function argument?
negative_passages.docid: 85731
negative_passages.text: Prove by induction that $n! > n^2$
negative_passages.docid: 144732
negative_passages.text: If $[G:H]=n$, then $g^{n!}\in H$ for all $g\in G$.
negative_passages.docid: 26837
negative_passages.text: Limit of the sequence $\{n^n/n!\}$, is this sequence bounded, convergent and eventually monotonic?
negative_passages.docid: 57398
negative_passages.text: Where does TREE(n) sit on the Fast Growing Hierarchy?
negative_passages.docid: 79847
negative_passages.text: proving of inequality $(n!)^2 \leq n^n\cdot n!\leq (2n!)$, where $n\in \mathbb{N}$
negative_passages.docid: 78190
negative_passages.text: How to prove that for all natural numbers, $4^n > n^3$?
negative_passages.docid: 66272
negative_passages.text: Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?
negative_passages.docid: 45914
negative_passages.text: Proving that $n!≤((n+1)/2)^n$ by induction
negative_passages.docid: 27580
negative_passages.text: Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$
negative_passages.docid: 136274
negative_passages.text: $n! \leq \left( \frac{n+1}{2} \right)^n$ via induction
negative_passages.docid: 133384
negative_passages.text: Question regarding to canonical factorization of $n!$?
negative_passages.docid: 55494
negative_passages.text: Proving Asymptotic Barrier - O notation for $\ln(n!)$
negative_passages.docid: 70336
negative_passages.text: Radius of Convergence of $\sum\ z^{n!}$
negative_passages.docid: 75373
negative_passages.text: Show that $2^n>n$ for $n\in \mathbb{N}$
negative_passages.docid: 24403
negative_passages.text: Prove that $ n < 2^{n}$ for all natural numbers $n$.