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Keith's user avatar
Keith's user avatar
Keith
  • Member for 9 years
  • Last seen more than 8 years ago
9 votes

For which infinite dimensional real normed linear spaces $X$ , can we say that every infinite dimensional subspace of it is closed in $X$ ?

7 votes

If $\frac{a}{b}<\frac{c}{d}$ and $\frac{e}{f}<\frac{g}{h}$, then $\frac{a+e}{b+f} < \frac{c+g}{d+h}$.

6 votes
Accepted

Do there exist continuous functions $f,g: \mathbb{R} \rightarrow \mathbb{R}$ such that $f(g(x))=x^2$ and $g(f(x))=x^3$ for all $x \in \mathbb{R}$?

5 votes
Accepted

Self Teaching Theory for Olympiad. Need advice for books.

5 votes

Polynomial whose one of its roots is $\cos(\pi/7)$

5 votes
Accepted

Why memorize trig identities?

5 votes

Subgroup of order 3

4 votes
Accepted

How do you calculate variables as exponents in a polynomial without a calculator?

4 votes

Solving for $x$ in $A=B\cdot \cos(x)+C\cdot \sin(x)$

3 votes
Accepted

For a ult (unit low. tri.) matrix A, can we transform $[A|I]$ into $[I|A^{-1}]$ only using row operations that correspond to ult elementary matrices?

3 votes
Accepted

Roots of $p(x)=\prod_{i=1}^{2n}(x-d_i)+k^2, \ \ \ \ n\in\mathbb N,\ k\in\mathbb R$

2 votes
Accepted

Equivalent definitions of symmetry group of regular n-gon (dihedral group)

2 votes
Accepted

Does being distance-preserving force affinity?

2 votes
Accepted

Change of order of integration of a triple integral

2 votes

Differentiation with dependent variable

2 votes
Accepted

Recommendation about studying calculus.

2 votes

What is the meaning of 'recursive' in Boolos, Burgess and Jeffreys? (Computability and Logic)

2 votes

Number Theory- Mathematical Proof

2 votes

Minimum and Maximum values of variance

2 votes
Accepted

what is wrong with this proof? (proving the transitive property of Big O)

2 votes
Accepted

Proving $(p \oplus q) \oplus r=p \oplus (q \oplus r)$

1 vote

Let $\left| {{a_{ii}}} \right| > \sum\limits_{i \ne j} {\left| {{a_{ij}}} \right|} $.Why does $A$ is nonsingular? .

1 vote

Difference between intersection of infinite sets having finite, and having infinite elements

1 vote
Accepted

What kind of geometry is useful to study for mathematical competitions?

1 vote

Looking for elementary proof of "for a circle, $C^2/A = 4 \pi$"

0 votes

Non-constructive proof that $\sum_{j=1}^n j^k$ is a polynomial $p(n)$ of degree $k+1$

0 votes

Solution Verification: $\; o(G) = p^n$, $p$ is a prime, and $ N \neq (e) $ is a normal subgroup of $G$. Then $N \cap Z \neq (e)$.

0 votes
Accepted

Proof of a exercise problem from basic set theory

0 votes
Accepted

Minimum number of locks and keys