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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.

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mathematical notation for defining a variable inside a conditional expression

I have the following conditional expression on $f$ and I want to use a variable which is only used inside the expression. I'm wondering what would be the best typset for defining it there. Here is the expression and $\beta$ needs to be defined…
ehsan
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Iterating through the same set twice in the same equation

I have a question regarding set theory when using forall on the same set twice, in the same equation. More specifically, this is the equation I want to write: $ \forall u_i \in U : u_i \; mutual_{reach} \; \forall u_k \in U $ What this should mean…
Bouet
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Symbol to represent "On the unit sphere" to laymen

I am preparing a deck of slides related to quantum computing for network-administrator and business type people which involves the following diagram: In the text I had $|\Psi> \in \{0,1\}$. I imagine this is fine for a non-mathematical audience,…
Mike Ounsworth
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Iverson Bracket / Conditional Sum of a string

I'm trying to turn calculations that I've been using on a data set into mathematic notation to write it down in a research paper. One of my calculations creates a factor that determines how often a certain value (in this case the geographic location…
leee
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Should I write $x (f(x))^{-1}$ with less parenthesis.

In this case, $x$ and $f(x)$ belong to a multiplicative group. I would like to write $x f(x)^{-1}$ instead of $x(f(x))^{-1}$. I figured that I could explain once what I mean by $x f(x)^{-1}$ and then use it freely after that. Is this acceptable?
Steven Alexis Gregory
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Notation for a function from all members of a tuple minus one.

Is there any compact, mainstream notation for a function from all members of a tuple minus one? What I have in mind is $f\left(a_{1},\ldots,a_{n}\right)$ (except for $a_{i}$) $=a_{i}$
Schiphol
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Is interval a set?

Given a function $f$; $$ f(x) = \frac{x}{1+x^2} $$ the support of $f$ is $$ \mbox{supp}f=\begin{cases} \overline{\{(-\infty, 0), (0, \infty)\}}=(-\infty, \infty)=\mathbb{R}&&(1)\\ \overline{(-\infty, 0) \cup (0, \infty)}=(-\infty,…
Danny_Kim
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How to write single definition for two indexed matrices in a single line?

I want to define $X_i$ and $X_j$ as $X_{i} = \left\{x_k| {x}_k \in \mathcal{C}_{i} \right\}$ and $X_{j} = \left\{x_k| {x}_k \in \mathcal{C}_{j} \right\}$ How can I combine these definition together in a correct notation? Something like the…
M.Reza
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Meaning of a notation

What is the meaning of the notation . I cannot search for such questions on google.
user41736
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What is the best notation for this problem?

Assume you have defined variables $A$, $B$ and $C$ in the text. There is also a defined function $f$ that applies on those variables. In addition you may have some variables such as $\kappa_A$, $\kappa_B$ and etc. The question is, how to best…
ehsan
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Does $\beta_{0,i}$ mean the same as $\beta{_0}_i$?

I have two vectors of variables, $X$, and $\beta_0$ that I am writing about. Each are indexed by $i=1,\ldots,n$ If I want to talk about $X_i$ and $\beta_{0_i}$, using \beta_{0_i}, the $i$ on the beta is too small to see. Even if I use \beta{_0}_i:…
Abe
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Are there any proposals for special parentheses for function arguments?

A few times, I wanted to highlight that a variable in the right-hand side of an equation depended on other variable. I can't recall a good example right now, but consider this one: $\tau = F d(\vec{r})\cos(\theta)$. Probably, the person who…
Leonardo Castro
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Capital and small letter function notations

Why are some functions denoted by capital letters? For example, an ODE is represented by the equation $F(t, y, y',\ldots, y^n) = 0$. Here, what I understand is that F is actually a multivariate function. Similarly, for $dy/dx=f(x,y)$ if we…
Vikram
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Set Notation: How to denote ALL points in some space satisfying a condition?

I am integrating a function over the multidimensional domain $\Omega$, which is a subset of a larger domain $X$. Omega is defined by ALL points $x \in X$ that satisfy some condition, the details of which are not important, that I will denote…
okj
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Notation conversion help with respect to combinatorical proof

First off, I wouldn't bring this to SO, but my teacher refuses to teach me notation. Anyhow... I'm doing a proof. The proof says: "Show that $8^n - 3^n$ is a multiple of 5 for all non-negative integers $n$. How do I say this in notation? I've…
Chris
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