![Examples of continuous functions $f:(0,1)\to[0,1]$ [closed]](https://edu.smbbmcl.edu.pk/uploads/examples-of-continuous-functions-f-0-1-to-0-1-closed_720.jpg)
Examples of continuous functions $f:(0,1)\to[0,1]$ [closed]
Hi so the question is asking if if there is a continuous function over $(0,1)$ which will result in the image $[0,1]$. Thank you so much! Explanations are...
22 Apr 2026 1 READS
Archive: General
What is the correct way to think about quotient sets and equivalence relations?
Perhaps there is not a correct way to think about it but I would want to know how others think about it. Here are my problems/questions, after my definiti...
22 Apr 2026 1 READS
square inscribed in a right triangle
A square of maximum possible area is circumscribed by a right angle triangle ABC in such a way that one of its side just lies on the hypotenuse of the tri...
22 Apr 2026 1 READS
![Irrationality of $r\sqrt{5}$ for rational number $r$? [duplicate]](https://edu.smbbmcl.edu.pk/uploads/irrationality-of-r-sqrt-5-for-rational-number-r-duplicate_720.jpg)
Irrationality of $r\sqrt{5}$ for rational number $r$? [duplicate]
As $5$ is a prime number, thus $\sqrt{5}$ is an irrational number. Now I am thinking about how to prove - If $r$ is a rational number, then how do we prov...
22 Apr 2026 1 READS
Binary floating-point representation of 0.1
If $b=10$ and $p=3$, then 0.1 is represented as $1.00 × 1/10$. If $b=2$ and $p=24$, then 0.1 cannot be represented exactly, but is approximately $$1.10011...
22 Apr 2026 1 READS
What did I do wrong in this double integral calculation?
I tried solving the double integral below, but I get the wrong answer. According to Symbolab, it should be $\frac{\sqrt{\pi}}{8}$. Can someone take a look...
22 Apr 2026 1 READS
Is $x = \arccos ( \frac{3}{5})$ a rational number?
Wolfram tells us $x = \arccos ( \frac{3}{5})$ is an irrational number. How can we prove it? (Without using a computer obviously)
22 Apr 2026 1 READS
![Why is the period of $\sec$ and $\csc 2\pi$ instead of $\pi$? [closed]](https://edu.smbbmcl.edu.pk/uploads/why-is-the-period-of-sec-and-csc-2-pi-instead-of-pi-closed_720.jpg)
Why is the period of $\sec$ and $\csc 2\pi$ instead of $\pi$? [closed]
Hi and thanks in advance. When $\tan x = \frac{(2x + 1)\pi}{2}$, the function is undefined, resulting in a period of simply $\pi$. However, $\csc$ and $\s...
22 Apr 2026 1 READS
Proving a CDF is cadlag
I'd like to know if this proof is correct. Thank you for your help. Let $X$ be a random variable. A function $F_X: \mathbb{R} \to [0,1]$ defined by: ...
22 Apr 2026 0 READS
Why is the exterior algebra a bi-algebra (and even a Hopf algebra)?
According to the wikipedia, the exterior algebra of a $\Bbbk$-vector space $V$ is initial with respect to being unital and there existing a $\Bbbk$-linear...
22 Apr 2026 1 READS
