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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.

12848 questions
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Formal notation for function equality

Is there a short-hand notation for $$ f(x) = 1 \quad \forall x $$ ? I've seen $f\equiv 1$ being used before, but found some some might (mis)interpret that as $f:=1$ (in the sense of definition), i.e., $f$ being the number $1$.
Nico Schlömer
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What does this notation, $x>x_0(\epsilon)$, mean?

What does this notation, $x>x_0(\epsilon)$, mean? I have seen this in several proofs and haven't quite figured it out.
Fred Daniel Kline
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Is there a mathematical symbol for "once"?

I've found a couple symbols that include the concept of once, like "the list of values which appear only once" and stuff like that. Is there a symbol that just means "once" or "one repetition" or "single"? Like, "f() happens one time." (sorry if the…
Matt
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Does order matter when dealing with quantifiers?

Do ${\forall}x{\forall}y{\exists}z$, ${\forall}x({\forall}y{\exists}z)$ and $({\forall}x{\forall}y){\exists}z$ all mean the same thing?
user285146
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Does the colon in function notation stand for "such that"?

The colon mark sometimes stands for "such that". When writing functions, it is customary to write, for example: $f:[0,1]\rightarrow[0,1]$. Can the colon in this context be interpreted as "such that"? If not, is it just a historical quirk that ":" is…
user46234
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What is the symbol that is used for the universal set in these two textbooks?

From this textbook: And this textbook: It looks like a squiggly E (\mathcal{E}) or perhaps it is the Greek letter xi (ξ). But I am not sure.
user46234
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Are there "variables/unknowns" for operations?

We use letters for unknowns/variables: $x^2=4$ Are there variables/unknowns for operations too? $8 \star 7 $ With the $\star $ being any operation.
Red Banana
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What do these dot-related symbols mean?

I was browsing the Puzzling.SE site when I came across this little challenge. The idea is to prove that 2016 is a "self-composable" number, i.e. that it can be computed using a given set of operations, and its digits only. Basically, using 2, 0, 1…
John WH Smith
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Is there a standard symbol for difference in order of magnitude?

Is there a standard notation, symbol(s) or other shorthand for representing the difference in order of magnitude between two numbers? Given the function... $$ f(x, y) = \log(x/y) $$ So f(1030, 55) ~= 1.272. Is there a standard notation to say "1030…
Eric Lease
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Question on meaning of a symbol: long thin C

I don't know how to write it in $\LaTeX.$ It is a tall skinny bold C. This is the context: A set is defined by: where $\complement\atop{\smash \scriptstyle i}$ is the thing I don't understand. The $i$ is actually directly underneath the weird $C$…
098765
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What does the notation $|B(x;\epsilon)|$ mean?

What does the notation $|B(x,\epsilon)|$ mean? Is it the volume of the open ball? I saw it from the following: ...It follows from the Lebesgue theory that for almost every $x\in\Omega$, $\lim_{\epsilon\to 0} \frac{1}{|B(x,\epsilon)|}…
3x89g2
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Sequence of points that is dense in a compact set.

I am reading a proof of Tietze extension theorem from a book Deimling - Nonlinear functional analysis, page 6. What is the plain meaning of following sentence: "Since $A \subset \mathbb{R}^n$ is compact, there exists a dense and at most denumerable…
Hulkster
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Standard notation for class of lipschitz continuous functions?

What is the widely used notation to denote the class of Lipschitz continuous functions? i.e. suppose $f$ is continuously differentiable, then $f \in C^1$
Fraïssé
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Notation: Vectors in a Matrix

In my lecturer's notes, he made use of the notation $$\begin{pmatrix}|&|&|\\\mathbf u&\mathbf v&\mathbf w\\|&|&|\end{pmatrix}$$ to denote a matrix which is made up of the vectors $\mathbf u$, $\mathbf v$ and $\mathbf w$. He states in the notes that…
Luke Collins
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What is the meaning of plus sign above brackets?

I was wondering what the meaning of the notation $\ ( )^+ \ $is? For instance, what would be the value for $\ (x)^+ \ $for different values of x, say: $\ x=-1, x=0, x=1 \ $? Thank you in advance. The original expression I encountered is a little…
Story Maths
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