# Tagged Questions

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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4answers
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### Any commutative associative operation can be extended to a function on nonempty finite sets

This is a fact we use very frequently in general mathematics when we write such notations as $1+2+3+4$: since we know that $+$ is commutative and associative, we can just "drop the parentheses" and ...
1answer
34 views

### Set Notation (Axiom of Replacement)

This question is related to the one I asked yesterday here in that it's related to another one of the Zermelo-Fraenkel Axioms. After looking over the notation used to describe the axiom, that is:  ...
1answer
28 views

### On Landau notations

How common it is to write e.g. $1-o(1)$ for a function that eventually approaches $1$ from below (or eventually equals $1$)? Would a better notation be $1-|o(1)|$ or what is meant is already obvious ...
1answer
54 views

### Is there a name for this given type of matrix?

Given a finite set of symbols, say $\Omega=\{1,\ldots,n\}$, is there a name for an $n\times m$ matrix $A$ such that every column of $A$ contains each elements of $\Omega$? (The motivation for this ...
0answers
68 views

### Working with subsets, as opposed to elements.

Especially in algebraic contexts, we can often work with subsets, as opposed to elements. For instance, in a ring we can define $$A+B = \{a+b\mid a \in A, b \in B\},\quad -A = \{-a\mid a \in A\}$$ ...
2answers
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### Set Notation (Axiom of Infinity)

I'm having trouble understanding the notation used in describing the axiom of infinity (which is number 6 in the Wolfram MathWorld page). I understand what the axiom is saying, but I'm trying to ...
0answers
12 views

### Complex representation and Dual representation notation

Let's say we have a representation $\rho$ of $G$ on a vector space $V$. Wikipedia refers to the dual representation as $V^*$, but the dual vector space as $\overline{V}$. It does the opposite for the ...
0answers
18 views

### Notation for Hadamard division

What is a reasonable notation for Hadamard division of two matrices? Several forum threads point to $\oslash$ as a possibility, but it feels "forced", for lack of a better word (I might go with a ...
2answers
47 views

### What exactly does this physically mean?

Let X(w) be a real random variable on ($\Omega$ , P). The image X($\Omega$) the set of all the values X(w) can take ,written $\Omega^{X}$. For any set $B \subset \Omega^{X}$ the probability of the ...
1answer
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### Confusing symbol in papers on hybrid logic

In literature about hybrid logic I'm reading for my thesis I've come across the following symbol: ::= Now, I've never seen this notation before. I can also not ...
3answers
42 views

### How to interpret summation signs

I'm taking a course in statistics, and I really need to brush up my math to be able to follow the book at times. I'm looking at formulas for sum of squares, and I am slightly confused about the ...
0answers
48 views

### Pronunciation of $H^{1}(G, M)$

How does one say the cohomology group $H^{1}(G, M)$ out loud in a talk/lecture? Do people just say "H1 of G comma M"?
1answer
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### “The whole is greater than the sum of its parts” as a mathematical expression [closed]

I'm trying to come up with a coherent way to express the saying "The whole is greater than the sum of its parts" using mathematical constructs. The second half of the statement (greater than the sum ...
1answer
46 views

### Mathematical Symbol

In the following paper, what does the symbol $\Phi$ in equation $3.1$ (page $3$) represent? Does it represent the normal distribution?
3answers
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### Using $p\supset q$ instead of $p\implies q$

I saw that a use for the notation $p\supset q$ instead of $p\implies q$ that got me a bit confused. One occurrences is in this Wikipedia link. It seems to me opposite than what it should be, let me ...
1answer
39 views

### Is it a standard to say that $a \oplus a_{\small 1}=0$ or $a \veebar a_{\small 1}=0$?

I am trying to express the following: $a$ or $a_{\small 1}=0$ but only one of them equals zero. so if $a=0$ then $a_{\small 1}\neq 0$ and if $a\neq 0$ then $a_{\small 1}=0$. And I'm ...
1answer
15 views

### Notation minimum of a column vector

I'd like to know the notation to express the minimum of a column vector. Is this notation correct? \begin{equation} \min \left[\matrix{ \left|b_{n}-b_{n+1}\right| \cr ...
2answers
101 views

### Is it an abuse of notation to omit the leading zero in a decimal less than 1?

Is it acceptable to write $.001$ rather than $0.001$ when using decimal notation? Are there contexts in which omitting the leading zero is acceptable, and other situations in which it is not?
1answer
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### What is the equivalent of a diagonal in a non-square matrix or array?

I have a non-square matrix $M$, that looks something like this: $M=\left[ \begin{array} & a & b & c \\ d & e & f \\ g & h & i \\ j & k & l \\ \end{array}\right]$ ...
0answers
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### Definition(s) for variable binding in first-order logic

The following statement made me realize that variable binding can be defined in first-order logic: The same holds for λ terms to define functions. There is no reason that they could not be ...
1answer
36 views

### Confusion over calculus notation (differentials/derivatives)

I have read from multiple sources that dy/dx is not to be interpreted as a ratio as the idea of 'dy' and 'dx' themselves will lead to logical difficulties. However, I have seen in many areas (e.g. ...
9answers
1k views

### How to represent the floor function using mathematical notation?

I'm curious as to how the floor function can be defined using mathematical notation. What I mean by this, is, instead of a word-based explanation (i.e. "The closest integer that is not greater than ...
3answers
100 views

### What is the meaning of the parentheses in $\phi^{-1}\left[\{\phi(g)\}\right]=gH=Hg$?

I am studying homomorphisms is groups and i saw a theorem saying: For $g$ in a group $G$, the cosets $gH$ and $Hg$ are the same, and collapsed onto the single element $\phi(g)$ by $\phi$. That is, ...
1answer
32 views

### How to use a clamp function / median in mathematical notation?

I'm writing some mathematical equations that describe some computations in my program and it's pretty important that it's written correctly. At one point, it clamps or truncates a value, $x$, into the ...
2answers
208 views

### Notation: Why write the differential first?

From reading answers here, I've noticed that some people write integrals as $\int dx \; f(x)$, while other people write them as $\int f(x)\;dx$. I realize that there is no mathematical difference ...
3answers
88 views

### Should I put interpunction after formulas?

I am presently doing my first substantial piece of mathematical writing, hence this, probably somewhat silly, question. How does display-style mathematics interact with punctuation? More ...
6answers
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### $(\mathbf{u}^T\mathbf{v})\mathbf{v} = \mathbf{u}^T(\mathbf{v}\mathbf{v})$ doesn't hold for $\mathbf{u}, \mathbf{v}\in\mathbb{R}^n$ - why?

Suppose I have vectors $\mathbf{u}$ and $\mathbf{v}$ in $\mathbb{R}^n$. It is well defined to write $5\mathbf{v}$ or $c\mathbf{v}$ for scalar $c$. Since the inner product of $\mathbf{u}$ and ...
2answers
124 views

### What is the first cardinal number which is greater than $\omega$ [closed]

What is the first cardinal number which is greater than $\omega$? How to denote it? Thank you very much. ADDed: Thanks Brain and Quinn for explaining for me. However, honestly saying, the ...
2answers
94 views

### What does “-2E-07x” means? [duplicate]

I'm a programmer who had always been lacking some mathematical skills, yes it's a shame, I know. I'm making this little software for a biologist friend, and at some point I need to pull out a graph ...
0answers
25 views

### Can anybody recommend a comprehensive source for understanding mathematical notations?

I foten struggle with understanding some of the mathematics written down in papers. This stuggle is often due to notation used. Therefore, I was wondering whether somebody is aware of a resource that ...
0answers
33 views

### Resources for learning formal math notation

Does anyone know of some resources that provide a good introduction to common notation used in formal math? For example, I honestly don't know how to interpret $f: \mathbb{Z} \rightarrow \mathbb{Z}$. ...
6answers
95 views

### Function Notation

due to our national cirriculum (the way in which it was taught in high school). We just said that f(x) means a function. Though I understand this isn't necessarily correct? In high school we used ...
2answers
202 views

### What does the notation $\twoheadrightarrow$ mean?

I don't know what this double-arrow $\twoheadrightarrow$ means!
1answer
43 views

### What's the difference of naming a polynomial ring as $\mathbb{C}\{ x,y\}$ and $\mathbb{C} [x,y]$?

I sometimes see both notations and I am led (maybe misled) to believe that they are the same thing. What is the formal difference between both of them? Or there isn't any?
2answers
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### Matrix rows notation

I'm working with a set of $M$ vectors $\{\mathbf{w}_i \in \mathbb{R}^N, \, i = 1, \ldots, M \}$. Since single vectors are usually considered as column vectors, I'm defining a matrix  \mathbf{W} = ...
1answer
42 views

### Is this the correct notation?

$\left [ \left \{ 1,2,3,4 \right \}! \right]^{-1}$Is this the correct notation if one wanted to obtain the factorial for each number in a sequence and then take the sequence and inverse each number in ...
9answers
574 views

### What could be better than base 10?

Most people use base 10; it's obviously the common notation in the modern world. However, if we could change what became the common notation, would there be a better choice? I'm aware that it very ...
0answers
20 views

### Notation for Space of Multilinear Functions

I'm in doubt if there is some "standard" notation for the space of multilinear functions on the cartesian product of $p$ vector spaces $V_i$ with values in another vector space $W$. I have seem for ...
0answers
41 views

### Frequency of Math Symbols [duplicate]

Does anyone know of a study that has calculated the frequency of math symbols based on some popular mathematics journals or math corpus? For example in English you have letter frequencies of the most ...
2answers
111 views

### Frequency of Math Symbols

Does anyone know of a study that has calculated the frequency of math symbols based on some popular mathematics journals or math corpus? For example in English you have letter frequencies of the most ...
1answer
62 views

### what does z subscript something mean

Decide a positive integer $N \in\mathbb Z$. Generate a uniformly distributed random positive integer sequence: $$v_1, v_2, \ldots,v_n\in\mathbb Z_N$$ My question is, what does $\mathbb Z_N$ really ...
1answer
35 views

### Any name for an isosceles triangle sides

Is there an English translation for Finnish words kanta and kylki? Namely, if $ABC$ is an isosceles triangle with $AB=AC$ then $BC$ is kanta in Finnish and $AB$, $BC$ are both kylki.
1answer
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### What is being maximised in the channel capacity formula?

The channel capacity formula is given as such: $$C=\max_{p(x)}I(X,Y)$$ Does this mean that it is the maximum probability multiplied by the mutual information, or is something else being maximised ...
3answers
51 views

### Difference between $\land$ and braces

I was wondering what are the difference between the $\land$ and $\begin{cases} \\ \\ \end{cases}$ symbol. As I know, they both mean "and". So far, I've noticed the $\land$ on statements (not sure ...
2answers
49 views

### Probability notation

Hey guys, I was just wondering why in my textbook(A First Course in Probability, 8th edition) and basically everywhere I've looked at when we have some random variable(assume for the sake of the ...
2answers
43 views

### Elementary Set Theory - Relations

I'm not exactly sure what to search for this problem I'm having, as I don't know the keywords, so I figured the best action would be to ask a question. I have this question: ...
2answers
53 views

### What does $\mathbb{\bar C}$ denote in complex analysis?

What does $\bar A$ denote when $A \subseteq \mathbb{C}$? I've seen it used in some places as the algebraic closure, other places as $\bar A = A$ \ $\partial A$ and other places again as \$\bar A = ...
2answers
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### Notation for number of value changes in a sequence

Let $A=\{a_{1}, a_{2}, a_{3}, a_{4}, ...,a_{n}\}$ be a finite sequence , where $a \in \mathbb{N}$. I would like to know the notation for something similar to a change rate. If I programmed, what I ...
2answers
36 views

### Summation and Product Bounds

If I have a sum or product whose upper index is less than its start index, how is this interpreted? For example: $$\sum_{k=2}^0a_k,\qquad \prod_{k=3}^1b_k$$ I want to say that they are equal to the ...
1answer
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### Should brackets be placed around an exponentiated factorial?

For example, one can derive an approximation of $\pi$ from Stirling's approximation with one additional term as $$\lim_{n \to \infty} \frac{72n(n!)^2}{n^{2n} e^{-2n} (12n+1)^2}$$ but is it correct ...
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