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Oct
13
comment Prove sequence converges
See here: Convergence infinite product.
Oct
12
comment What is the dimension for this subspace?
From $x-y-z=0$, you get $z=x-y$. Hence, using the first equation, $0=x+y+z=x+y+(x-y)=2x$, which means $x=0$. Both equations reduce to $y=-z$. Then any vector in $S$ must be of the form $\lambda(0,-1,1)$.
Oct
12
comment Show that $b$ must be a power of $a$ when $a$ is an $n$-cycle.
What have you tried?
Oct
9
revised Continuous on an interval implies continuous on every subinterval?
Edited tags
Oct
9
suggested suggested edit on Continuous on an interval implies continuous on every subinterval?
Oct
9
comment Continuity Question in Analysis
Hint: Use the definition of continuity at $a$ with $\varepsilon=\dfrac{f(a)}{2}$.
Oct
7
comment What does $ \sum_{i = 1}^{\infty} \frac{1}{i(i-1)!}$ converge to?
Hint 2: Exp...${}$
Oct
6
comment $f(x)=\frac{x}{1-|x|}$ is not uniformly continuous
Not necessarily. The image of $f$ would be bounded if, for instance, its domain were compact.
Oct
6
comment $f(x)=\frac{x}{1-|x|}$ is not uniformly continuous
$f$ is continuous.
Oct
4
comment Amateur Math and a Linear Recurrence Relation
Have you seen this wikipedia page?
Oct
3
comment Show that any convex subset of $R^k$ is connected
Suppose $C$ is a non-empty convex set and that $C=U\cup V$ where $U,V$ are two disjoint nonempty open sets. Take two elements in $C$: $a\in U$, $b\in V$. Since $C$ is convex, define $\alpha:[0,1]\to C$ by $\alpha(t)=a(1-t)+tb$. Since $\alpha$ is continuous and connectedness is preserved by such functions, $\alpha([0,1])=P$ is connected, but $P\cap U$ and $P\cap V$ are two disjoint nonempty open sets whose union is $P$. This is a contradiction.
Oct
3
comment Show that any convex subset of $R^k$ is connected
What do you know about connectedness?
Oct
2
comment Can the components of a continuous injective function fail to be injective?
If $\boldsymbol{x,y}\in \Bbb R^n$, then $$f(\boldsymbol{x})=f(\boldsymbol{y})\iff (f_1(\boldsymbol{x}),\ldots,f_m(x))=(f_1(\boldsymbol{y}),\ldots,f_m(\boldsymbol{‌​y})) \iff f_i(\boldsymbol{x})=f_i(\boldsymbol{y})$$ for all $1\le i\le m$.
Oct
2
comment Always positive two variable function
That is information you must add to the question.
Oct
2
comment When does order of partial derivatives matter?
See here
Oct
2
comment Always positive two variable function
What else? We need more information to prove $f$ is always posiive.
Oct
2
revised Determinant n exponent
Added latex
Oct
2
suggested suggested edit on Determinant n exponent
Oct
2
comment Always positive two variable function
What do you know about $f$?
Oct
2
comment Studying for Abstract Algebra
Practice. Do as many problems as you can before the exam.