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
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Counterexample for false O notation statement

Stumbled upon some O notation counterexamples, but can't seem to figure out which one would disprove this statement: For any positive constant $c$, $f(cn)\in O(f(n))$. Any help would be appreciated!
user481532
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subscripts on the left side of a number

I encountered this strange notation in an online set theory course. I've emailed my instructor, but he's on vacation so I was wondering if any of you knew what it meant. Apparently it equals 8. Edit: Here's a complete question involving the notation…
push33n
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Arrow notations "⥊" and "⥋"

I'm wondering what the following arrows are typically used for and what do they signify: ⥊ (U+294A; "Left barb up right barb down harpoon"; \leftrightharpoondownup (mnsymbol package)) ⥋ (U+294B; "Left barb down right barb up harpoon";…
andselisk
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How do I write this in proper notation?

I was wondering if anyone could help with the below. I don't usually write maths so I'm not even sure what I'm trying to search for. I want to write the below as a single equation because in reality C and J are quite large terms. $V_1=C+J_2$ and…
Kat Bailes
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Notation for "Amount of significant sign changes in interval"

I want to define a good notation for the number of how often the function $f:\mathbb{R}\rightarrow \mathbb{R}$ changes its sign in the interval $I\subset \mathbb{R}$ significantly. By significantly I mean that the function changes its sign forgiven…
Thilo
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Notation for function mapping between cases

Suppose I have a function $f$ which can take different mappings depending on how $f$ is parameterized. For example, I want to write something like this: \begin{equation} \label{eq4:bounds_ex1} f: \begin{cases} \mathbb{R}^n \rightarrow \mathbb{C}, &…
Johnny Que
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Notation for mapping a vector and variable

So I have a function $f(x,y)$ where $x \in \mathbb{R}^n$, $y$ is a real variable, and $f(x,y)$ is a complex function of these variables (where for a given vector $x$ and given $y$, the function $f$ is a complex number). For example, if $x =…
Johnny Que
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Notation for mapping with bounded independent variable

So I have a function $f(x,y)$ where $x\in \mathbb{R}^n$ and $y\in \mathbb{R}$, but bounded (i.e., $y \in [-a,a]$). Now, I want to write something like $f:\mathbb{R}^{n+1} \rightarrow \mathbb{R}$. But how would you express this if the variable $y$ is…
Johnny Que
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Notation for mapping

So I have a function $f(x,y,z)$ where $x,y\in \mathbb{R}$ and $z \in \mathbb{R} \cup \{\infty \}$. Now, I want to write something like $f:\mathbb{R}^3 \rightarrow \mathbb{R}$. But the thing is that $z$ includes $\infty$...So what is the correct way…
Johnny Que
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List members of the set: $\{x: (x \in\mathbb{Z})\land(x^2<8) \}$

I have this problem: $$\{x: (x \in\mathbb{Z})\land(x^2<8) \}$$ Originally I thought the solution was $\{-4,-1,0,1,4\}$ but $-2^2$ is $-4$ not $4$ so the answer would be infinite. (my original assumption was that a negative number squared was…
blackcat47
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Set theory: A = ⟨1,→⟩, is '→' equivalent to '∞'?

I'm reading an introductory mathematics book and came across the following syntax: A = ⟨1,→⟩ B = {1,2,3} The question: Find A ∩ B and A ∪ B Should I assume A = ⟨1,→⟩ = ⟨1,∞⟩?
Xunie
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Looking for notation that extends the dimension of a vector

I am wondering if there is any notation for the following operation of a sort of concatenation of vectors. For example if I have a vector $x=(x_1,\dots,x_n)\subseteq\mathbb{F}^n$ and $y\in\mathbb{F}$ is there any notation for extending $x$ into…
Ltoll
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logarithmic potential of harmonic moment

What is the symbol behind the integration means in logarithmic potential ? Let's say $$x_{\mu}(z)=\int_D \ln|z-\xi|d\mu(\xi)$$ What does $\xi$ means ? I have been studying harmonic moment and I come across this term.
hong wai
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Notation for node in directed edge

What is the common way to specify the first node in a directed edge. Let's say I have: $$e= \left$$ How can I refer to the first node in $e$? $e[1]$ is common in programming but what is the common notation in math world?
Oren Roth
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Help with notation (stupid question)

I need to understand the following formula: $$u_{i}=\frac{x_i-\overline{x_i}}{{||x_i-\overline{x_i}||}_2}$$ I don't know the notation: $${||x_i||}_2$$ Is it the second moment? Please help me to convert it to sums and number of values. UPDATE I need…
zlon
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