Linked Questions

4
votes
3answers
2k views

What does $]a,b[$ mean? [duplicate]

I recently encountered the above notation for sets, and I've never encountered it before. What does it refer to?
1
vote
0answers
1k views

Alternative interval bracket notation? [duplicate]

I am reading a computer science paper and have come across some notation that I am unfamiliar with. it says to consider functions from $\mathbb{R}^N$ to $]-\infty,\infty]$ is this the same as ...
0
votes
1answer
133 views

bracket of intervals [duplicate]

I know $[0,1]$ denotes the interval between 0 and 1 with the boundary. And $(0,1)$ denotes the interval between 0 and 1 without the boundary. Today, I encounter some expressions as $]0,1]$, $]-\infty,+...
2
votes
1answer
97 views

What is the meaning of the notation $]1, 1[$? [duplicate]

This may look like a silly question but I am struck in my work with this notation in one of the papers. What is meant by $]1,1[$ ?
0
votes
0answers
44 views

What does the interval $]-\frac{\pi}{2},\frac{\pi}{2}[$ mean? [duplicate]

It could be a misprint or typo in what I'm reading, but I just want to make sure. I'm reading Loring Tu's "An Introduction to Manifolds", and at the end of the first chapter, one of the problem ...
15
votes
3answers
5k views

What does the notation $[0,1)$ mean?

I am studying the procedure for bucket sort from Introduction To Algorithms by Cormen et al, which assumes that the input is generated by a random process that distributes the elements uniformly and ...
2
votes
1answer
1k views

What's the difference between ]a,b[ and (a,b)?

Is there any difference between $]a,b[$ and $(a,b)$? If there is no difference, what would be the motivation of using $]a,b[$ over $(a,b)$?
2
votes
2answers
91 views

Why $\bigcap_{n=1}^\infty ]0,e^{-n}[=\emptyset$?

Why is: $$\bigcap_{n=0}^\infty\,\mathopen{]}0,e^{-n}\mathclose{[}\,=\emptyset\quad?$$ Indeed, $$\forall n\in\mathbb N, 0\in\mathopen{]}0,e^{-n}\mathclose{[},$$ and thus $0\in\bigcap_{n=0}^\infty\,\...
1
vote
2answers
127 views

Excluding interval from N

I've recently been learning factorials in school. If there is an equation (in $\mathbb N$) with $(n-5)!$, I have to ensure that $n$ is not 1, 2, 3 or 4. I've been told that I should write domain: $D =...
1
vote
1answer
171 views

Domain and range of a cyclometric function

My textbooks tells me: $$f(x) = \arctan(x)$$ $D_f = \mathbb{R}$ and $B_f = \left\langle -\dfrac{1}{2} \pi, \dfrac{1}{2} \pi \right\rangle$ $$g(x) = \arcsin(x)$$ $D_g = [-1, 1]$ and $ B_g = [ -\...
2
votes
2answers
157 views

Let $\alpha:\langle a,b\rangle \longrightarrow \mathbb{R}^2$ be a continuous function and injective

Let $\alpha:\langle a,b\rangle \longrightarrow \mathbb{R}^2$ be a continuous function and injective how to prove that $\alpha (\langle a,b \rangle )$ has empty interior ? Any hints would be ...
3
votes
0answers
68 views

Notation $(a,b)$ for $]a,b[$.

Is there any logic or justification for the notation $(a,b)$ to represent $]a,b[$? To me this notation is very ambiguous and confusing because it looks like a couple of numbers and not an interval. ...
1
vote
1answer
50 views

Story of 'point' inside of rectangular triangle

Yesterday when I was solving some basic geometry problems, I was curious ( I'm still though! ) about something: Why / When do some people indicate the angle with its measure $= 90^\circ$ by adding a ...