How to correctly compate $f(n)$ and $g(n)$ when working through $O(n)$ notation?
Going through theory, missing the idea, need a bit of help. So, the initial state is: $$f(n) = O(g(n))$$ Assume that $f$ and $g$ are both nondecreasing an...
Category: Updates
How to rigorously find range of a function?
What is a rigorous method/mechanism to find the range of a function $f(x)$? Is it acceptable to find $f^{-1}(x)$ and then its domain? I understand that $f...
![To prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not uniformly converge to $f(x) = 0$ on $[0,1]$](https://press.oye.mlga.ek.gov.ng/uploads/to-prove-that-f-n-x-frac-nx-1-n-2x-2-does-not-uniformly-converge-to-f-x-0-on-0-1_720.jpg)
To prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not uniformly converge to $f(x) = 0$ on $[0,1]$
My Approach. To prove the given statement it is sufficient to show that $$\exists \epsilon > 0, \exists x \in [0,1], \forall N \in \mathbb{N}, \exists ...
Using logic laws to verify the logical equivalences
I need to use theorem 2.1.1 in order to verify the following: ∼((∼p ∧ q) ∨ (∼ p ∧ ∼q)) ∨ (p ∧ q) ≡ p I applied the Double Negative Law to get ((p ∧ q) ∨ (...
Calculus I Optimization Problem - Maximization of Profit
Calculus problem that I've been trying to get my head around. Problem: A company can sell 20 products if it charges $40 per product. For each dollar ...
Weierstrass M-test proof?
Let (X,d) be a metric space. For each n $\epsilon$ N let $g_n$:X$\rightarrow$R be a continuous function. Let ($a_n$) be a sequence of positive real number...
Interpretation of log differences
I have a very simple question. I am confused about the interpretation of log differences. Here a simple example: $$\log(2)-\log(1)=.3010$$ With my present...
Linear transformations and polynomials
I've been having a really hard time recently understanding linear transformations. I would really like to know conceptually what exactly is going on....
How do you pronounce $\hat{n}$?
I've found a symbol $\hat{n}$ in an equation, and I have no idea how to pronounce it, and how to write it phonetic. Edit: I've found it here: ht...
Maximize area of a triangle with fixed perimeter
If perimeter of a triangle is $2d$, what is the length of sides so the triangle has maximal area? I found some solution using circle and angles, but I thi...
