![Open Cover / Real Analysis [duplicate]](https://news.conceivablytech.com/uploads/open-cover-real-analysis-duplicate_720.jpg)
general
Open Cover / Real Analysis [duplicate]
I have the next question: Let $K \subset $ $R^1$ consist of $0$ and the numbers 1/$n$, for $n=1,2,3,\ldots$ Prove that $K$ is compact directly from the de...
Apr 10, 2026
Archive: General
general
Is $x^x$ a polynomial, an exponential or both?
If $c$ is a constant, and $x$ is a variable, we'd say that $f(x) = x^c$ is a polynomial function of order $c$. Conversely, the function $f(x) = c^x$ ...
Apr 10, 2026
general
Find the length of $CE$
In quadrilateral $ABCD$, $AB=6$, $\angle{ABC}=90°$, $\angle{BCD}=45°$ and $\angle{CAD}=2\angle{ACB}$. If $DE$ is perpendicular to $AC$ with $E$ on side $B...
Apr 10, 2026
general
Can someone please explain the cube to sphere mapping formula to me?
I am wondering if anyone could explain how the following formula works, it is supposed to take the input as a point on a cube then map that to points on a...
Apr 10, 2026
general
What is logical consequence and logically equivalent in discrete math?
I'm having a difficult time understanding what the meaning are with these two. Is it correct if I have (P ⇒ Q) ∧ P and I say Q is a logical consequen...
Apr 10, 2026
general
How to prove $A \subset B \iff A \cup B = B$
Let A, B be two sets. Prove that $A \subset B \iff A \cup B = B$ I'm thinking of using disjunctive syllogism by showing that $\neg \forall Y(Y \in A)...
Apr 10, 2026
general
Related Rates problem, xy=4
$xy=4$ $a)$ Find $\dfrac{\mathrm dy}{\mathrm dt}$ when $x=8$, Given $\dfrac{\mathrm dx}{\mathrm dt} = 10$ $b)$ Find $\dfrac{\mathrm dx}{\mathrm dt}$ when ...
Apr 10, 2026
general
How would I show this bijection and also calculate its inverse of the function?
I want to show that $f(x)$ is bijective and calculate it's inverse. Let $$f : \mathbf{R} \to \mathbf{R} $$ be defined by $f (x) = \frac{3x}{5} + 7$ I...
Apr 10, 2026
general
Isn't square root a bit like Log()?
I want start by saying that my math skills aren't great and I'm trying to learn. I took a look at square root. Squaring the number means x^2. An...
Apr 10, 2026
general
What is an example of function $f: \Bbb{N} \to \Bbb{Z}$ that is a bijection?
Could you give me an example of function $ f \colon \mathbb N \to \mathbb Z$ that is both one-to-one and onto? Does this work: $f(n) := n \times (-1)^n$? ...
Apr 10, 2026
