query: Argue that $n!$ dominates any polynomial function of $n$, i.e., $n^x = O(n!)$ for any real $x$.
positive_passages.docid: 147849
positive_passages.text: Does $(n!)/n^{1000}$ diverge or converge
negative_passages.docid: 48260
negative_passages.text: If $R=K[X]/(X^n)$, can represent any element as polynomial with degree $<n$
negative_passages.docid: 135614
negative_passages.text: Show that $2^n > n^2$ whenever n>4.
negative_passages.docid: 146506
negative_passages.text: If a complex function $f$ is Entire, and there exist $k,R > 0$, $n \in N$ such that $|f(z)| > k|z|^n$ for all $|z| > R$, then f is a polynomial.
negative_passages.docid: 83036
negative_passages.text: f(g(x)) has a degree divisible by n
negative_passages.docid: 154487
negative_passages.text: Maximal number of monomials of multivariate polynomial
negative_passages.docid: 124901
negative_passages.text: Big-O notation and polynomials
negative_passages.docid: 62177
negative_passages.text: Prove that: $2^n < n!$ Using Induction
negative_passages.docid: 12166
negative_passages.text: How many irreducible polynomials of degree $n$ exist over $\mathbb{F}_p$?
negative_passages.docid: 78190
negative_passages.text: How to prove that for all natural numbers, $4^n > n^3$?
negative_passages.docid: 145519
negative_passages.text: Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$
negative_passages.docid: 13083
negative_passages.text: If for a polynomial $P(k) = 2^k$ for $k = 0, 1, . . . , n$, what is $P(n+1)$?
negative_passages.docid: 9997
negative_passages.text: For what powers $k$ is the polynomial $n^k-1$ divisible by $(n-1)^2$?
negative_passages.docid: 72735
negative_passages.text: Understanding the proof of a formula for $p^e\Vert n!$
negative_passages.docid: 45914
negative_passages.text: Proving that $n!≤((n+1)/2)^n$ by induction
negative_passages.docid: 127547
negative_passages.text: Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.
negative_passages.docid: 79359
negative_passages.text: Show that $f$ is a polynomial if it's the uniform limit of polynomais