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Sep
9
answered Prove that $\sin(x+a), \sin(x+b),\sin(x+c), \hspace{5pt} a,b,c \in \mathbb{R}$ are linearly dependent
Jul
31
answered Let $T:V\to W$ be a linear transformation. If $\dim V> \dim W$ then $T$ is not injective. True or false?
Jul
10
answered The annihilator of an intersection
Jun
4
answered Why doesn't mathematical induction work backwards or with increments other than 1?
May
23
answered If $AB = I$ then $BA = I$
Apr
4
answered How to understand Cauchy's proof of AM-GM inequality(the last step)
Mar
25
answered Riemann-integrable functions and pointwise convergence
Mar
14
answered Is mathematics a science?
Jan
20
answered How to show these two definitions of the Riemann integral are equivalent?
Jan
7
answered Prove that $ x^n - y^n = (x-y) (x^{n-1}+x^{n-2}y\,+ \,\,…\,\,+ y^{n-1})$
Dec
28
answered A proof of Artin's linear independence of characters
Dec
13
answered Proof by induction that $\alpha^n + \beta^n \in \mathbb Z$
Dec
3
asked Multiplicative nature of the separability degree
Nov
23
answered $F$ field, $\alpha$ separable on $F$. Is $F(\alpha)$ a separable extension of $F$?
Nov
14
answered Showing that the characteristic function of $\Bbb Q$ is not Riemann Integrable
Nov
3
answered Show that $F(E^p)$ consists of all linear combinations of elements in $E^p$ with coefficients in $F$.
Nov
2
answered Prove that the function $f:\mathbb{Q}(\sqrt{2}) \to \mathbb{Q}(\sqrt{2})$ given by $f(a + b \sqrt{2})=a-b\sqrt{2} $ is an isomorphism.
Nov
2
answered Does convergence in $L^p$ and pointwise imply the same limit?
Nov
2
answered Suppose $\{f_k\}$ is a sequence of $M$-measurable functions on $X$. Let $p_1$ and $p_2\in [1,\infty)$, and suppose $f_k\in L^{p_1}\cap L^{p_2}$.
Oct
22
answered Propositional Logic: Models/Counter-Models