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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Meaning of notation $\mathbb{A}^{\mathbb{R}\times\mathbb{R}}$

I am familiar with notation like $\mathbb{R}^x$ (meaning the set of all x-tuples with real elements) $\mathbb{A}\times \mathbb{B}$ (being the set of all pairs whose first element is from $\mathbb{A}$ and second element from $\mathbb{B}$. But what…
Ubiquitous
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Can union notation be simplified

Just for context consider something like a set $\lbrace X_i \rbrace_{i \in I}$ where $I$ is also a set. I must say I'm more familiar with the sequencial notation $(X_i)_{i \in I}$ but I guess this makes it less of a set-related question. Should we…
James Well
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Notation: Vector-valued sequence space

I'm struggling with the notation for space $\mathcal{X}$ of N-tuples of elements of $\ell^2(\mathbb{Z})$, where $\ell^2(\mathbb{Z})$ is the space of sequences of finite energy. As an example, the following $\mathbb{x}[n]$ is an element of the space…
Maximilian Matthé
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Symbol for WLOG

Does anybody know a commonly used symbol for WLOG (without loss of generality)? I'm not comfortable with typing the whole thing every time and the abbreviation is just a compromise. If there is one for QED, why shouldn't there be one for WLOG? :)
Count Zero
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Notation for a number with no repeating digits

I'm currently working on a problem for which I'd like to include a mathematical definition. I'm an amateur, so please correct me if anything is already wrong. The set of possible solutions for $x, b \in \mathbb{N}$: $$M_b = \{x \in \mathbb{N} :…
padarom
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Notation for a placeholder function that maps to other functions

I'm trying to write a very general equation to calculate some $Value$ which relies on a context-dependent function $g$. How do I concisely communicate that $g$ maps to different functions under different contexts? So far I…
tetris11
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Notation for similar/related functions

Suppose I have two functions: $f(x)$ and $g(x)$ These functions are similar -- meaning, they are variations of the same general thing. I want to express to the reader that they are similar/related. I tried superscripts: $f^{variation1}(x)$ and…
kevinpeterson
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Prove that $\prod_{i=2}^n (1-1/i^2) = {n+1\over 2n}$

prove the $$\prod_{i=2}^n (1-1/i^2) = {n+1\over 2n}$$ for all n greater or equal to 2. $\pi$ should be a big pi from $i=2$ to $n$ for $(1-1/i^2)$. I'm really confused about the $\prod$ function. UPDATE: Suppose$$\prod_{i=2}^n (1-1/i^2) = {n+1\over…
Jack F
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For any two points, there exist a path of $n$ segments that connects them. Is there a name for this kind of set?

We consider a set $A$. $A$ is called convex if for every $x,y\in A$, we have the line segment $xy$ is also in $A$. I want to generalize this notion, such that instead of one line segment, there can be $n$ line segment, where $n$ is some fixed…
Chao Xu
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How can this algorithm be expressed in mathematical terms?

I have found a solution to a basic problem using an algorithm, but I'm having a bit of a hard time expressing this algorithm in terms of discrete math. for (i=2; i<=2004; i+=2) { if (i%8 === 0 || i%11 === 0 ) tall.push(i); } I'm thinking that…
Ярослав Рахматуллин
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Notation in identification function

The notation I have does not fall with the notation in the wiki link and I want to see I understood. Can I expand the following idicator function: $$ 1\{x\leq 0\}x$$ in the following way? $$1 = \begin{cases} x & \quad x\leq 0\\ 0 &…
havakok
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What is $\sum_{k, l}$?

For example, when you have an expression like this, $\sum_{k, l} g^{kl}$, what is this sum if one wrote it out?
Borol
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How to denote a function that depends on $a_1, \ldots, a_n$ without the dots?

I know that I can wrote something like $$a_1 + \cdots + a_n$$ without the dots as $$\sum_{i=1}^n a_i$$ which seems clearer to me. As a programmer, I'd rather have a rule set with variables than something with dots where I have to extract the pattern…
Martin Ueding
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Meaning of product with bar (\Gemini-symbol)

In chapter IV, paragraph 2 of Neukirch's Class Field Theory he writes The adeles form a ring, denoted by $$\mathbb{A}_K = \prod_\mathfrak{p} K_\mathfrak{p}$$ where addition and multiplication is defined componentwise. Except, he doesn't write…
Krijn
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Product of $(x-1)(x-2)(x-3)\ldots (x-k+1)$

I was working on a formula, and along the way, I came across this product:$$(x-1)(x-2)(x-3)(x-4)\ldots(x-k+1)\tag1$$ This is just a quick question, but Question: Is there a shorthand notation for $(1)$? I mean, besides writing all of the terms…
Frank
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