Let $f : \mathbb{R} \to \mathbb{R}$ such that $f$ is an open map. Is it true that $f$ is continuous??I am unable to find a counterexample (I think it is false)Thanks for the help!!
If $f_1=O(g_1)$ and $f_2=O(g_2)$ then $$\frac{f_1}{f_2}=\frac{O(g_{1})}{O(g_{2})}=O(\frac{g_1}{g_2})$$ I want to show this relation is true or not.ThanksNow, you would need $\Omega(\cdot)$ for $f_2$. Intuitively: you need an upperbound (i.e., $O(\cdo
Consider the Circulant Graph $Ci_{2n}(1,n-1,n)$ as described here:http://mathworld.wolfram.com/MusicalGraph.htmlAnother way to describe $Ci_{2n}$ would be $2n$ vertices with vertex set$V=\{a_0, \dots , a_{n-1}, b_0, \dots , b_{n-1}\}$and with edge se
Here is T:T = a v ¬b, ¬a v (c^d), b I am suppose to use resolution calculus to prove that T |= d ^ b holds.As in the first step, we translate T into a set of clauses, all clauses being in CNF.My lecturer converts T into the following clauses:Clause 1
We have a short assignment on the described question and I already have gone through a lot of trash results from Google. I can't seem to find any.I don't know where else to post this question. Please guide me! It will be a great help.
If we suppose that we have a polynomial $q(x)$ of the following form:$q(x) = \sum_{i=0}^N{c_i x^i} \text{ where } c_i=0 \text{ or } c_i=1$In other words, if we are given a polynomial with binary coefficients (either 0 or 1), what is the probability t
If we have a set of primes $p_1$, $p_2$, ... , $p_n$, we can easily construct a function of their product:$$f(\alpha) = \alpha \left( \prod_{k=1}^n{p_k} \right) + 1$$I'm wondering what the probability is that this function equals a prime. I want to s
If $f_1=O(g_1)$ and $f_2=O(g_2)$ then $$\frac{f_1}{f_2}=\frac{O(g_{1})}{O(g_{2})}=O(\frac{g_1}{g_2})$$ I want to show this relation is true or not.Thanks
Use the definition of convergence of a sequence to show $$\lim \frac {2n^2}{n^3+3}= 0$$ I understand that to do this we must show $ \frac {2n^2}{n^3+3} \leq \varepsilon$, but I'm not sure how to do that.
Prove or disprove that $d(f,g) = ({\int_0^1 |f(x)-g(x)|^{2}dx})^{1/2}$, on $C[0,1]$ is a metric. If so, describe the $\varepsilon$-neighborhood.Do you know that for $f\in C[0,1]$ $$||f||_2=\left(\int_0^1|f(x)|^2dx\right)^{1/2}$$ is it's euclidean nor
Is $\mathbb{R}$ an open ball in $\mathbb{R}$?If we write B(0,$\infty$) as the open ball then $\mathbb{R}$ is an open ball in $\mathbb{R}$. Is it correct?Thanks.No, balls have finite radius. It is an open set however.1 4
We've got the following game:You roll two dices. You get paid equal to the number rolled.Additionally, if you roll doubles, you reroll (Same rules apply to that roll. That means there's not limit to how much you can win).What's the expected payment o
When calculating summation of series I use these methods ;Ex: Method One $$U_r=\frac{1}{(r-1)r(r+1)(r+2)}$$$$U_r=\frac{1}{(r-1)r(r+1)(r+2)}\left[\frac{(r+2)-(r-1)}{3}\right]$$ Then $$U_r=\frac{1}{3(r-1)r(r+1)}-\frac{1}{3r(r+1)(r+2)}$$Then clearly $$U
A reduction of $10%$ % in the price of sugar would enable a man to buy $2$ kgs of sugar more for Rs.$125$. Find the reduced price per kg.My attempt: Let the initial price of sugar be Rs. $x$ kg.Price after $10%$ % reduction $$=x-10 percent of x$$ $$=
Let $s$ and $t$ be odd integers. Show that $st$, $s^2-t^2/2$ and $s^2+t^2/2$ are relatively prime. I've seen this question on here, but unfortunately some of the cases were not covered, and I want to confirm that the way I'm proving it is correct bec