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.

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Alternative interval bracket notation?

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 writing $(-\infty,\infty]$? to use another example, is…
Gus Kenny
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writing a formulation in a smaller form

Is it possible to write this in a smaller form: $(A \neq \emptyset) \vee (B \neq \emptyset)$ ? is it for example mathematically correct to write it as: $A \vee B \neq \emptyset$ ?
shn
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using a formula to make a statement with the use of greater than, less than symbol

I am trying to make statement using the greater than less, less than symbol. I am unsure if the use of $\lt\gt$ symbols have to facing the same direction in an equation. Could you say: $x \lt x + y \gt y$ would this mean that $x$ is less than $x+y$…
Melissa RN
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function, vertical line and two values (notation for evaluation at 1 point or 2 endpoints)

What does it mean when you have notation like this $$F\bigl(g(u)\bigr)\Bigr|_0^t,$$ where $F$ and $g$ are some general functions?
user1066113
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Is there a symbol with values 0 and 1 depending on parity of a parameter

Is there a reasonably standard symbol depending on a parameter, like $\delta_i$ or something, that takes the value $1$ when $i$ is even and $0$ when $i$ is odd? or the other way around? $$ \frac{1 + (-1)^i}{2} $$ is far too cumbersome. Edit: I…
Barry Smith
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Sum without an index

Is $\sum a$ a customary (standard) shorthand for $\sum_{i\in\operatorname{dom}a} a_i$, where $a$ is an indexed family of say integers?
porton
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How to denote a function of all but one parameter (notation question)

Say I have $n$ variables, $x_1,\dots,x_n$ and $n$ functions $f_i$ such that $f_i$ is a function of $x_1,\dots,x_{i-1},x_{i+1},\dots,x_n$, but not $x_i$. Is there a more compact way of denoting this than $$f_i(x_1,\dots,x_{i-1},x_{i+1},\dots,x_n) =…
Joey91
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What's the difference between $\sum_{r=1}^n(ar+b)$ and $\sum_{r=1}^nar+b$

Does $$\sum_{r=1}^n(ar+b)=\sum_{r=1}^nar+b$$ or does $$\sum_{r=1}^n(ar+b)=\sum_{r=1}^nar+\sum_{r=1}^nb$$ If I'm given $u_r=ar+b$ how would I substitute that into $$\sum_{r=1}^nu_r$$ Does that mean…
Thomas Winkworth
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Notational question

We are in the framework of measurable transformations, i.e. let $(X,\mathcal{B},m)$ be a measure space and let $T:X\to X$ be a measurable transformation. In your opinion, what does the following notation mean? $$ T^{-n}(A)\qquad\text{for}\quad…
avati91
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About order of an index

I have a simple question on precedence of operators, especially applying a function and an index. Can we write $q(F)_i$ (without an additional pair of parentheses) for $(q(F))_i$? Maybe, it would be better $q(F)(i)$? What is the best way to denote…
porton
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How to create a set with the results of a function?

Let $A$ and $B$ be sets of elements and $f()$ be a function that according to a condition return one or more associations $(a_k,b_k)$ that comply that condition otherwise if there is not any association it returns $\emptyset$. Which notation could I…
user206695
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Notation for denoting one argument fixed and acting upon the other

Given a function $f_1:\mathbb R^n\mapsto \mathbb R$, and a fixed vector $v\in \mathbb R^n$ I construct another function $f_2:\mathbb R^n \times \mathbb R^n\mapsto \mathbb R$ such that $f_2(d,v):=f_1(T(v) \cdot d)$ where $T(v)$ is some transformation…
Mohammad Alaggan
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Is $\frac{1}{ \frac{1}{x-1}}$ equivalent to $x-1$ when $x=1$?

Is $\frac{1}{ \frac{1}{x-1}}$ equivalent to $x-1$ even when $x=1$?
YoTengoUnLCD
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What do superscripted numbers inside parentheses on functions mean?

I have a function $G(t) = (tx + (1 - x))^p = \sum\limits_{k=0}^pB_k^p(x)t^k$. I must find two different expressions for $G^{(j)}(1)/j!$. What does the superscript $(j)$ mean in this case?
sveinungf
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The names of two unfamiliar operations

I am currently researching a QR-based root finding algorithm encountered two operations that I don't understand. I'd love to look them up, but I can't find the names of these operations/notations. The first was an unfamiliar usage of a colons and…
Dizzy
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