Suppose $u,v$ in $V$. Prove that $ = 0$ iff $||u||$ is at most $||u+av||$
34147
$\|u\|\leq \|u+av\| \Longrightarrow \langle u,v\rangle=0$
20192
Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
63889
Prove that if $u_n\rightarrow \infty$ then $\frac{1}{u_n} \rightarrow 0$
85739
Show that $f(x) = 0$ for all $x \in [a,b]$ given $|f'(x)| \leq C|f(x)| $
106408
Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).
138212
Please help me prove: $v(a+b)\leq v(a)+v(b)$, and $v(ab)\leq v(a)v(b)$ where $v(x)=\inf{\{\vert x^n \vert}^{1/n}: n\in\mathbb{N}\}$
136789
How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?
43504
Proving the existence of a complement subspace $U' \subset V$.
25981
Prove that $\sum_{k=0}^n a_k x^k = 0$ has at least $1$ real root if $\sum_{k=0}^n \frac{a_k}{k+1} = 0$
76347
Shorter proof for some equvalences
40564
Prove that $u(x,t)=\int_{-\infty}^{\infty}c(w)e^{-iwx}e^{-kw^2t}dw\rightarrow 0$ if $x\rightarrow \infty$
85239
Proof $dim(W)=dim(V)=n \implies W=V$
36771
How to prove that A is normal if and only if there's a unitary matrix V,s.t. A*=AV?
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
3433
Proof if $a \vec v = 0$ then $a = 0$ or $\vec v = 0$
59872
How to prove $\inf(S)=-\sup(-S)$?
105852
How to verify whether or not there exists a vector $x$ such that $Ax > 0$?