Question 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.

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37 views

Best books about notation

I am reading A History of Mathematical Notations and I would love to read further about the trends and advantages of different notations in mathematics, pure or applied. Is there any good book or ...
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0answers
39 views

Derivative Notation as a factor

In the figure below, the author uses the notation D to replace the Leibniz's notation d/dt, and after that he rewrites the equation, disconnecting the symbol of the derivative, D, of its function, ...
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1answer
23 views

What is the notation (if any) for series probability inclusion?

In statistics, what is the notation to use for an event $A$ in $B$ in $C$ in $D$, etc., where the series may continue for a large number of events? The following works for a few events: $$A\cap B\cap ...
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0answers
78 views

Funny translations of mathematical words [closed]

As already noticed in this question there are some mathematical words that literally translated from a language to english (or from english to this language) means something totally different. A few ...
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1answer
70 views

How to translate math technical terms?

What is a good way to translate mathematical technical terms? This can sometimes be hard because some words have different meanings in some language. For example: "eigenwert" (= "eigenvalue" ...
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1answer
20 views

Conditional Probability Notation

I am writing a piece of work and have a situation where I have a 'double' conditional. e.g. The event of Y = y conditional on X = x; the event X = x is also conditional on parameter z. What's the ...
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1answer
49 views

Question about necessary and sufficient conditions?

I am working on a question which begins with The number $\alpha$ is a common root of the equations $x^2+ax+b=0$ and $x^2+cx+d=0$. Given that $a\neq c$, show that $$\alpha=-\frac{b-d}{a-c}$$ ...
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0answers
15 views

Flow Notation over Interval

Given a section of the flow $\Phi^t(x_0)$ (for finite $t$), I'd like to denote a subsection of this flow from times $\tau^{i-1}$ to time $\tau^{i}$ using similar notation. I was considering using ...
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1answer
16 views

Specific order sequence as subset of other sequence

I have a certain fitness function that evaluates a sequence. An example of such a sequence is: $h = [2\ 3\ 7\ 5\ 4\ 6]$. The fitness function is defined to be $0$ if the route $h$ does not include the ...
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2answers
25 views

Describing Notation of a set with an odd gradient

Hello how can you describe such a set: M = { 1 2 5 10 ...} The gradient is always odd in steps of 2 Gradient 1 + 3 + 5 + 7 + ... How can you describe such a set? I need somehow 2 variables to ...
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2answers
65 views

Is there a proper term for these?

The 'square root' sign is formally the 'radical symbol'. 'Brackets' are formally 'parentheses' Is there a formal term for the 'fraction sign' or say the 'absolute value bars'? EDIT: I can see some ...
2
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0answers
30 views

Can I denote $f'(g(x))=\frac{\text{d}}{\text{d}(g(x))} f(g(x))$?

Can I denote $f'(g(x))=\frac{\text{d}}{\text{d}(g(x))} f(g(x))$? Wikipedia avoids this by letting $y=f(u), u=g(x)$ and then denoting $f'(g(x))=\frac{\text{d}y}{\text{d}u}$.
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4answers
64 views

What does P in blackboard bold type of letter stand for? ℙ?

In the first post of the thread "Cardinal number subtraction", Cardinal number subtraction there is a symbol for some kind of set which looks like this: ℙ I am familiar with symbols for natural ...
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0answers
26 views

Notations for interior product

There are two symbols in the Unicode "Supplementary Mathematical Operators" range whose names intrigue me 2A3C: INTERIOR PRODUCT: ⨼ (like $\lnot$ upside down) 2A3D: RIGHTHAND INTERIOR PRODUCT: ⨽ ...
2
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0answers
73 views

About the differential notation in measure theory

Is there any good reason for which integrating according to a measure includes a $\mathrm d$ as in $\int f\mathrm d\mu$ ? Or is it just a manner to keep formal consistency with the traditional ...
2
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1answer
18 views

In notation for argmin

I saw this notation for $\in$ -- I'm assuming this means "defines", right? $$\hat{\theta} \in \underset{\theta}{\operatorname{argmin}} \dfrac{1}{2} \sum_{j=1}^n (\theta^T x^j - y^j)^2$$ Does anyone ...
2
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2answers
17 views

general sum notation considering also not incremental indexing

I need to write a formula with summation in a general case allowing also the case with not incremental indexing. Example: $ \sum_{i=\underline{i}}^\bar{i}$ where can be ...
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1answer
69 views

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 $x=1$?
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0answers
16 views

Help understanding Wiener filtering formula

I would like some help interpreting the following formula, equation 1 from this paper: https://www.math.uni-bielefeld.de/~rehmann/ECM/cdrom/3ecm/pdfs/pant3/strela.pdf $\hat{X} = ...
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3answers
79 views

Can $a|b$ be used to mean $a$ can be divided by $b$? [closed]

Commonly $a|b$ means $a$ divides $b$, and I've seen $a\vdots b$ be written to mean $a$ can be divided by $b$ (meaning $b$ divides $a$). But how often would there be ambiguity if you wrote $a|b$ to ...
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1answer
20 views

Understanding notation of sets

What does it mean if you have a set suppose it is denoted $\theta = R \times (0,\infty)$. I'm a bit confused what the $\times$ represents?
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3answers
88 views

Mid '|' in math?

What does this equation mean? What does the $|$ mean? $446617991732222310 | mn(m^k - n^k)$ Here is the complete question for reference - What is the smallest positive integer $k$, such that for ...
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2answers
42 views

What's the notation for the intersection of stabilizer subgroups on a subset?

Let $G$ acting on the the (finite) set $S$, or the (finite dimensional) space $V$. Let $s \in S$, then the stabilizer $G_s:= \{ g \in G \ \vert \ gs = s \}$. Let $R \subset S$, then there are ...
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1answer
16 views

meaning of $f_{\chi_{E}}$

given $(X,\mathcal{M})$ a measurable space, I Have $E \subset X$ and $\chi_{E}$ is an indicator function. then what is meant by $f_{\chi_{E}}$ ? I am not very clear with this notation and meaning.
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2answers
53 views

Does \dots imply countable?

I am given an arbitrary set $S$. If I say the following: "Suppose that the elements of $S$ are labeled $x_1,x_2,x_3,\dots,$" am I notationally implying that the number of elements in $S$ is ...
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1answer
12 views

Expressing Sub-sequences of a sequence - notation

Given a sequence $b_n = \sin(\frac{n \pi}{2})$, I am trying to show that $(b_n)$ diverges. I have the idea down, I know exactly what to do, but just not HOW to do it. I know that any convergent ...
2
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0answers
24 views

Tensor notation in vectors

I have the following expression $\partial_{x_a}(\partial_{x_b} \rho \partial_{x_b}\rho) - \partial_{x_b}(\partial_{x_a}\rho\partial_{x_b}\rho)$ How do I write this in vector notation? At least the ...
2
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2answers
90 views

Quantifier for “there is at most one”?

As "there is at least one" and "there is exactly one" both have their symbols, I wonder what is the common notation for "there is at most one"? By "common" I mean the desired notation can be used ...
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0answers
20 views

Notation - continuity limit under an integral

I'm currently showing that the following integral is continuous: $$\int_{g_1(x)}^{g_2(x)} f(x,y) dy$$ Where $g_1, g_2, f$ are continuous. I am doing this by taking the following limit: $$\lim ...
6
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1answer
66 views

What does ∗⇒mean?

I am still really new to mathematical notations, and I am still having difficulty understanding most of the languages and notations. A recent notation I am very confused about ...
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42 views

Can I improve my Chain Rule (derivative) proof?

If $f'(g(x))$ and $g'(x)$ both exist, then $$f'(g(x))=\lim_{\Delta g(x)\to 0}\frac{\Delta f(g(x))}{\Delta g(x)}\stackrel{(1)}\implies \frac{\Delta f(g(x))}{\Delta g(x)}=f'(g(x))+\alpha(\Delta x),$$ ...
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0answers
35 views

What is this symbol ($\Vdash$) called?

This symbol: $$\Vdash$$ What is it called? It is often used in modal logic, like this: $W\Vdash$. I looked for it in wikipedia/modal logic and wikipedia/logic notation, but could not find it.
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1answer
40 views

What does the notation $U(\frak{g})[[\hbar]]$ mean?

I'm reading the following motivation for studying quantum group but I'm unfamiliar with the double bracket notation in $$U(\frak{g})[[\hbar]].$$ Is this a special set of polynomials with coefficient ...
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1answer
44 views

Nested radicals notation

Is there any convenient notation for things like: sqrt(1+sqrt(2+(sqrt(3+... Maybe using limits? I'm asking purely notational-wise.
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1answer
56 views

A few questions about derivative notation

$1)$ How do I denote derivative of $ax^2+b$ in terms of $ax^2$? $(ax^2+b)'(ax^2)$ can easily be confused with $ax^2\cdot(ax^2+b)'$. $2)$ How do I denote the derivative of $ax^2+b$ in terms of ...
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1answer
41 views

Can I denote derivative of $f(g(x))$ in terms of $g(x)$ by $f'(g(x))_{g(x)}$?

How to denote derivative of $f(g(x))$ in terms of $g(x)$ in prime (with $'$ without $\text{d}$) notation? Is it conventional to denote derivative of, say, $\sin(\cos x)$ in terms of $\cos x$ in ...
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3answers
85 views

What is meant by $\frac{d ^2y}{dx^2}$?

I have this homework question: Find $\frac{d^2y}{dx^2}$ for $y = (x^3−5)(2x+3)$. But I do not know why there are squares in $\frac{d^2y}{dx^2}$, so I cannot solve it. What is meant by this?
3
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0answers
43 views

Why is the boundary of a topological space $M$ denoted $\partial M$?

Why is the boundary of a topological space $M$ often denoted $\partial M$? Is there any connection between boundary and partial derivative?
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0answers
13 views

There is a logical or mathematical symbol for compatibility/incompatibility?

Exists a symbol in logic or mathematics to relate two or more compatibility or incompatibility conditions? I dont want to specify a determined area of study (topology, algebra, etc...) I just want to ...
0
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1answer
42 views

Which notation is correct

This one: \begin{align} V &= 100 + 1 \\ &\cong 100 \\ &\cong 50+50 \end{align} or \begin{align} V &= 100 + 1 \\ &\cong 100 \\ &= 50+50 \end{align}
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10 views

Notation for defining a total ordering with random tiebreaking

Suppose I have a set of 3-tuples $A = \{(3, 4, 5), (3, 4, 6), (2, 5, 7), (1, 1, 1)\}$. I want to define an ordering over elements in this set so that for two elements $x=(x_1, x_2, x_3)$ and $y=(y_1, ...
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1answer
39 views

What is the name of the following matrix “product” in which elements are not multiplied?

Assume that I am given the following matrices: $A = \begin{bmatrix} a_{1,1} & \dots & a_{1,n_a} \\ \vdots & \ddots & \vdots \\ a_{m_a,1} & \dots & a_{m_a,n_a} \end{bmatrix}$ ...
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1answer
26 views

Finding powers of prime ideals from its generators and understanding generator notation

I am trying to understand ideal notation with pointed brackets and how to use it. For instance, if I had an ideal $\mathfrak{a}=\left<2,1+\sqrt{-5}\right>$, where $2$ and $1+\sqrt{-5}$ are its ...
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1answer
72 views

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?
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1answer
29 views

Is there a quick way to notate 'any intersection of these sets is the empty set'?

Is there a quick way to notate 'any intersection of these sets is the empty set'? I have a number of sets, I want to express that none share any elements with any other. Is there a way to express ...
0
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1answer
40 views

Can someone identify this equations font in ACC paper? [closed]

I am writing a report, and want to use microsoft word 2013 to type the following equation: What type of font it use in microsoft word? (I know it might be written in Latex) (This ia a ...
2
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2answers
23 views

Linear transformation notation question

Well the question is pretty basic, but I am learning math on my own. And I cannot understand the notation of linear transformation. I understand what linear transformation is, its properties and what ...
1
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0answers
23 views

Notation for vector of expectations

I have $n$ 'types' in a population. The frequency of each type is given by a $1 \times n$ row vector $\boldsymbol{x} = (x_{1},...,x_{n})$ (I'm treating this a random vector). I also have an $n \times ...
1
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0answers
36 views

What is this notation $\odot$ for?

(Note that symmetric algebra and symmetric tensor do not coincide when the characteristic is not $0$.) I'm reading this aricle:http://en.m.wikipedia.org/wiki/Symmetric_tensor And here it defines ...
3
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0answers
40 views

Formulating equation for distances between atoms

I'm trying to formulate notation to describe code that calculates the distances between protein atoms (represented as points in 3D space). Fragments consist of residues (amino acids) and each residue ...