query: How to prove that $\max(f(n), g(n)) = \Theta(f(n) + g(n))$?
positive_passages.docid: 143900
positive_passages.text: how can be prove that $\max(f(n),g(n)) = \Theta(f(n)+g(n))$
negative_passages.docid: 88425
negative_passages.text: Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
negative_passages.docid: 110313
negative_passages.text: Prove that $\gcd(f(x),g(x)) = 1$.
negative_passages.docid: 12083
negative_passages.text: How to prove $\limsup (x_{n}+y_{n})=\lim x_{n}+\limsup y_{n}$?
negative_passages.docid: 84697
negative_passages.text: Show that if $|f(z)| \leq M |z|^n$ then $f$ is a polynomial max degree n
negative_passages.docid: 19804
negative_passages.text: How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
negative_passages.docid: 127242
negative_passages.text: $|A\times B|= \text{max}(|A|,|B|)$ for infinite sets
negative_passages.docid: 966
negative_passages.text: Show that $\lim_{n\rightarrow \infty} \sqrt[n]{c_1^n+c_2^n+\ldots+c_m^n} = \max\{c_1,c_2,\ldots,c_m\}$
negative_passages.docid: 93964
negative_passages.text: Proving that $f$ is a bijection from $N$x$N$ to $N$.
negative_passages.docid: 145181
negative_passages.text: How can I prove the maximum number of edges?
negative_passages.docid: 13253
negative_passages.text: Prove $f(S \cup T) = f(S) \cup f(T)$
negative_passages.docid: 98816
negative_passages.text: How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
negative_passages.docid: 154247
negative_passages.text: Proving $f(x)$ attains $\max$ or $\min$ when $f(x)\to0$ as $|x|\to\infty$.
negative_passages.docid: 70067
negative_passages.text: Asymptotics of $\max\limits_{1\leqslant k\leqslant n}X_k/n$
negative_passages.docid: 85535
negative_passages.text: Finding maximum of $|f'(i)|$
negative_passages.docid: 98399
negative_passages.text: Suppose $f$ and $g$ are entire functions, and $|f(z)| \leq |g(z)|$ for all $z \in \mathbb{C}$, Prove that $f(z)=cg(z)$.
negative_passages.docid: 118348
negative_passages.text: Let $x$ be transcendental over $F$. Let $y=f(x)/g(x)$ be a rational function. Prove $[F(x):F(y)]=\max(\deg f,\deg g)$