Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [notation]

Questions on the meaning, history, and usage of mathematical symbols and notation. Please remember to mention where (book, paper, webpage, etc.) you encountered any mathematical notation you are asking about.

Before asking a question on the site, please check if you can find your answer in Earliest Uses of Various Mathematical Symbols or the book A History of Mathematical Notations.

Alternatively, a textbook or paper usually takes the time to explain the notation they're using; please remember to mention where you've seen the notation you are asking about.

12848 questions
2
votes
1 answer

How to write down the order of a tuple

I want to write down the order of tuples $(a, b)$ with $a,b \in \{1,...,n\}$. What is a good way to do so? Right now I wrote: $(1,1),(1,2),\ldots,(1,n),(2,1),(2,2),\ldots,(2,n),(3,1),\ldots,(n,n)$ I'm unsure about the last part…
user1
  • 133
2
votes
1 answer

What does a circle above a variable mean?

If we carry out a linear coördinate transformation, $$x'_i=\sum_{k=1}^3c_{ik}x_k+\overset\circ x'_i,\quad i=1,2,3,$$ (from Introduction to the Theory of Relativity by Peter Gabriel Bergmann) I came across this in a book about relativity and…
Jannik Pitt
  • 1,980
2
votes
0 answers

Is there any notation to denote the solution of a particular equation?

Let's say that I have an equation: $$x + 2 = 7 + y$$ If I need the solution for $x$, I can solve it and then use $5 + y$. No problem there. But say I have an abstract equation. For now I am using the following to denote the equation:…
Anonymous
  • 457
2
votes
2 answers

If $\lim a_n$ does not exist, then does this mean that $\lim a_n\neq 0$?

If $\displaystyle\lim_{n\to\infty} a_n$ does not exist or if $\displaystyle\lim_{n\to\infty}a_n\neq0$, then the series $\displaystyle\sum_{n=1}^{\infty} a_n$ is divergent. From Stewart's Early Transcendentals Calculus. I would think that if the…
gz839918
  • 195
2
votes
3 answers

Is $x$ in $ax+b$ every value, or a specific unspecified value?

Given $ax+b$, we often draw a line $y = ax+b$ and we say this is for all values of $x$ and $y$, but is it wrong to say that $x$ is every value at the same time? For instance we say $x\in \mathbb{R}$. When we then say that $x=3$, are we introducing a…
Frank Vel
  • 5,339
2
votes
3 answers

How $f:[a,b]\rightarrow[c,d]$ should be read?

I found it in a book but I don't know what the ":" means. What does this expression mean?
Vitor Abella
  • 157
2
votes
2 answers

which natural english interpretation of this symbolic statement is correct?

Part of Keith Devlin's Coursera MOOC on mathematical thinking requires the translation of this symbolic statement into natural language: $$ 5 < x < 7$$ Interpretation 1: $x$ is a single unknown number located somewhere between 5 and 7 on the number…
Conor
  • 536
2
votes
1 answer

Best Notation for Introducing Finite Numbers of Elements

What is the best way to quantify over a finite number of elements of a set? For instance, suppose that one wished to quantify over $n$ real numbers $a_1,\ldots,a_n$ in order to state a property of their sum. In such a case, I often see authors…
emi
  • 1,640
2
votes
4 answers

What does the notation $z\in\mathbb{C}\backslash\mathbb{R}$ mean?

I know that $z\in\mathbb{C}/ \mathbb{R}$ means that the domain is the complex plane with the real line removed. What does the notation $z\in\mathbb{C}\backslash \mathbb{R}$ mean? EDIT: Turns out that I got things backwards. If $\mathbb{C}\backslash…
Kagaratsch
  • 2,239
2
votes
1 answer

Symbol to show that implication is one-sided

Sometimes A => B is true, but B => A is not true and this fact is important and not obvious. Is there a short symbol to write it in order not to write "A => B and not B => A"
sooobus
  • 710
2
votes
2 answers

Describing sets from running indices

For a paper I have a set of particles which I usually reference by $ p $. The paper is physics related, so I haven't made any real formal definition of the set, and always just relate to them as "the particles". I use it as $$ m_{i} = \sum\limits_p…
pingul
  • 155
2
votes
1 answer

What does the middle dot in parentheses mean?

The below picture is from section 3.3.1 in this paper; I'm not familiar with the notation of using middle dots in square parenthesis. Are the authors using this simply to indicate that any two parameters can be passed to the function K? Thank you,
aaronsnoswell
  • 524
2
votes
2 answers

Is there any difference between $\sum_{ij}$ and $\sum_i\sum_j\;?$

I was reading Tensors by Feynman, where he said: [...]$$u_P=\tfrac{1}{2}\sum_i\sum_j\alpha_{ij}E_iE_j\;.\tag{31.7}$$ The energy density $u_P$ is a number independent of the choice of axes, so it is a scalar. A tensor has then the property that when…
user142971
2
votes
4 answers

What does the mathematical symbol with an underline below the variable name mean?

I have been reading a research paper. The author has used a variable '$x$' with an underline beneath '$x$'. I know that a variable with a line on top of it implies it's arithmetic mean. But I have never seen a symbol with a line under the variable…
sajid
  • 133
2
votes
1 answer

Use of $\arg$ function

I know that $\underset{x}{\operatorname{argmax}}f(x)$ is defined as the value at which $f(x)$ has its maximum. There is also $\underset{x}{\operatorname{argmin}}$. However, in statistics, I often write something like $\Phi(z)=0.95$, and I am then…
Xiphias
  • 709
1 2 3
…
99 100