onurcanbektas

### Questions (373)

 48 If the field of a vector space weren't characteristic zero, then what would change in the theory? 18 If $A$ and $B$ are positive constants, show that $\frac{A}{x-1} + \frac{B}{x-2}$ has a solution on $(1,2)$ 10 Topologically, is there a definition of differentiability that is dependent on the underlying topology, similar to continuity? 10 True or false: If $f(x)$ is continuous on $[0, 2]$ and $f(0)=f(2)$, then there exists a number $c\in [0, 1]$ such that $f(c) = f(c + 1)$. 9 What if the basis not countable, then what?

### Reputation (3,572)

 +5 What does “assigning a Riemannian metric in a differentiable fashion” mean? +5 Explanation for the proof of Ptolemy-inequality +5 if the projection of $E\subseteq \mathbb{R}^n$ onto $\mathbb{R}^{n-1}$ has (n-1) dim. measure zero, then the set $E$ has $n$-dim. measure zero -2 If the tangents are parallel at each point for two curves, then so do their principal normal and binormal vectors

 5 The Pigeonhole Principle 3 I would like some help proving a (seemingly simple or obvious) lemma about quotient spaces of isomorphic vector spaces. 3 Recommended Book after Finite-Dimensional Vector Spaces by Halmos 3 $\mathcal{L}(V,W)$ is infinite dimensional when $V$ is finite dimensional and $W$ is infinite dimensional. 3 Prove that If $f(x)\to a$ and $f'(x) \to b$ as $x\to +\infty$, then $b = 0$

### Tags (268)

 8 linear-algebra × 104 6 pigeonhole-principle × 2 8 calculus × 32 5 linear-transformations × 52 7 real-analysis × 87 5 abstract-algebra × 22 7 derivatives × 31 5 proof-verification × 20 6 general-topology × 37 5 multivariable-calculus × 19

### Accounts (71)

 Mathematics 3,572 rep 11037 Academia 1,162 rep 21222 Science Fiction & Fantasy 835 rep 11338 Physics 815 rep 628 Travel 333 rep 17