# All Questions

1,393,750 questions
Filter by
Sorted by
Tagged with
8 views

### Monotone convergence theorem for a generic $f(x,y)$ instead of $f_n(x)$

I was wondering if it is safe to say that the monotone convergence theorem $$\lim_{n\to\infty} \int_X f_n(x) = \int_X \lim_{n\to\infty} f_n(x)$$ (where $f_n(x)$ is a non-decreasing sequence, etc.) is ...
5 views

### Finding integer solutions of K for equation floor(A/K) = B

How to find integer solutions of K for equation floor(A/K) = B, in terms of A and B where A and B are non-negative integers? What I tried: floor(A/K) = B then B <= A/K < B + 1 then BK <= A &...
7 views

### $\forall\delta, \sigma \in F$ where $\delta \land \sigma$ are contrad., $\exists\theta$ so that $\delta\land\neg\theta$ & $\sigma\land\theta$ contrad.

I'm in my first logic class ever and I'm trying to wrap my head around this obscure question... Show that for all pairs $\delta, \sigma \in F$, where $\delta, \sigma$ contradict themselves there ...
13 views

### Find the minimum value of the expression given that a,b,c are positive and real.

$${(a+3c)\over(a+2b+c)} + {4b\over(a+b+2c)} - {8c\over(a+b+3c)}$$ Here was my attempt: If c tends to infinity and a and b are small we get 1/3. Now , i took $b=0$ and we get $(a-c)^2\over(a+c)(a+3c)$ ...
13 views

10 views

10 views

### $Tor(A,B) = 0$ if $A,B$ is torsion free

I don't understand the proof given in Hatcher p.265 of $Tor(A,B) = 0$ if $A,B$ is torsion free. The proof is the following : The line I don't get is "This means [...] can be reduced to $0$ by a ...
### What is $DE.DA$ here?
In $\triangle ABC$, let $D$ be the midpoint of $BC$ and $E$ be a point on $AD$ so that $\angle BEC +\angle BAC = 180^\circ$. If $BC = x$, then find $DE.DA$. How to approach this? Please do not work ...