Mathematics Stack Exchange
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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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Notation for Nested Set

Let $A=\{a,b\}$. I'm looking for notation for $(A\times A)\;$,$\;(A\times A)\times (A\times A)$ , $((A\times A)\times (A\times A) )\times ((A\times A)\times (A\times A))$, and so on. I don't think ${A^{2}}^{2}$ is a clear notation because this can…
Chris
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What is the difference between black and white square in notation?

I'm reading a book on description logic and I found white and black squares at the end of some paragraphs. I would think they stand for Q.E.D., but since there are two types used in one book, I believe the black square states for something else.…
nuoritoveri
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Is this symbol used enough to have a name?

I'm not sure how to type it, so here's an image drawn using MS Paint: It's an equals sign and a question mark superimposed on each other. From the times I've seen the symbol, it asks if the LHS is equal to the RHS. If yes, then [do something]. If…
Allure
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How do you mathematically express a set of values that are all different?

Possibly a strange "why would you want to" question, but how do you mathematically express a set of values that are all different? For example, a set of values for which a mode calculation is impossible due to each element being unique.
Perry Collier
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Question On Modulo Notation

I understand what the Modulo/Modulus is and how it operates and everything, but a textbook is using some notation that I just can't quite grasp. Basically, we have the solution $(x,y) = (\pi($mod$(2\pi)),0)$ From the problem, clearly I can deduce…
Spaderdabomb
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Mathematical notation to expand a list/set of values?

Is there any mathematical notation to expand a list/set of values? I am looking for something that would expand like this: $A=(x=0,x<=3)[2x+1]$ $A=[2(0)+1,2(1)+1,2(2)+1,2(3)+1]$ $A=[1,3,5,7]$
YGranja
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What does the following notation mean: $ x \in [-1, 1]^{N}$?

What does the following notation mean: $ x \in [-1, 1]^{N}$ ? Does it mean that $x$ is either 1 or -1 ?
al27
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Are functions which say $X$ onto $Y$ mean the function is surjective?

Throughout my reading I've encountered theorems which use certain wording, which is unclear at times. For example, consider the following corollary taken out of Intro to Topology by Mendelson, Let $X$ and $Y$ be topological spaces, let $f:X\to Y$ be…
S.D.
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Function Definitions that Appear Circular

There are many instances where definitions of functions appear self-referential, but are in fact consistent and well-defined. Here are a couple cases: The proof of the existence of a maximal analytic continuation for a holomorphic function germ at…
Wayne
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Einstein's notation for matrix multiplication $G^{-1} B$

Let us define $G$ as the metric tensor and $B$ as a tensor compatible with metric tensor $G$. How can we denote $G^{-1} \, B$ in Einstein's notation? I know $g^{ij}$ is every entry of the inverse metric tensor and lower/upper $B_j^i$ is used on the…
Bruno Peixoto
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Which notation is correct/preferred for the squared form of the function: $ f_a(x)^2 $ or $f^2_a(x) $?

I have a function $f_a(x)$ with one independent variable $x$ and a parameter $a$; if I want to write the square form of this, which one is correct or preferred? $$ f_a(x)^2 \qquad \text{or} \qquad f^2_a(x) $$
sara96
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What does the colon mean in this probabilty equation?

$$ q\left(\mathbf{x}_{1: T} \mid \mathbf{x}_{0}\right)=\prod_{t=1}^{T} q\left(\mathbf{x}_{t} \mid \mathbf{x}_{t-1}\right) $$ What dose the $\mathbf{x}_{1: T}$ mean? This is from https://drive.google.com/file/d/1noQ2d4-nzSh3Yp3-mOOYN8YGJoSa4pmz/view…
LNseyJt2X-24UJ4r7KTL
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Is there a standard notation for the set of negative integers and zero?

There is $\mathbb Z^-$, $\mathbb Z^*$, $\mathbb Z^+$. There does not seem to be a notation for negative integers and zero.
KeithSmith
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Textbook Notation: Meaning of cf.

What is meant when an author gives an expression, labeled say $(3.4)$ and then immediately below writes: (cf. eq $3.2$)? i.e. what does the cf. stand for? Not sure this is completely necessary but for instance I am currently looking at the text…
Mjoseph
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Convenient notation for "is linearly proportional to"

Is there a convenient notation for "$A$ is linearly proportional to $B$"? I know that you could write something like $$\exists k,c\in \mathbb R : A = kB+c$$ but I'm thinking something along the lines of $A \sim B$ or $A \propto B$. I just want…
Matti P.
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