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.
6
votes
4answers
43 views
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 ...
4
votes
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:
$$ ...
1
vote
1answer
28 views
On Landau notations
How common it is to write e.g. $1-o(1)$ for a function that eventually approaches $1$ from below (or eventually equals $1$)? Would a better notation be $1-|o(1)|$ or what is meant is already obvious ...
5
votes
1answer
54 views
Is there a name for this given type of matrix?
Given a finite set of symbols, say $\Omega=\{1,\ldots,n\}$, is there a name for an $n\times m$ matrix $A$ such that every column of $A$ contains each elements of $\Omega$?
(The motivation for this ...
6
votes
0answers
68 views
Working with subsets, as opposed to elements.
Especially in algebraic contexts, we can often work with subsets, as opposed to elements. For instance, in a ring we can define
$$A+B = \{a+b\mid a \in A, b \in B\},\quad -A = \{-a\mid a \in A\}$$
...
3
votes
2answers
48 views
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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
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 ...
0
votes
1answer
36 views
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 ...
3
votes
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 ...
0
votes
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"?
0
votes
1answer
56 views
“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 ...
2
votes
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?
1
vote
3answers
54 views
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 ...
2
votes
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 ...
0
votes
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
...
3
votes
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?
3
votes
1answer
41 views
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]$
...
3
votes
0answers
34 views
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 ...
4
votes
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. ...
16
votes
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 ...
5
votes
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, ...
3
votes
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 ...
10
votes
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 ...
2
votes
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 ...
4
votes
6answers
84 views
$(\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 ...
-4
votes
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 ...
1
vote
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 ...
0
votes
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 ...
0
votes
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}$. ...
2
votes
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 ...
4
votes
2answers
202 views
What does the notation $\twoheadrightarrow$ mean?
I don't know what this double-arrow $\twoheadrightarrow$ means!
4
votes
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?
2
votes
2answers
34 views
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} = ...
1
vote
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 ...
20
votes
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 ...
0
votes
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 ...
1
vote
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 ...
4
votes
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 ...
1
vote
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 ...
2
votes
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.
0
votes
1answer
17 views
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 ...
1
vote
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 ...
1
vote
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 ...
0
votes
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:
...
0
votes
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 = ...
0
votes
2answers
19 views
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 ...
3
votes
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 ...
0
votes
1answer
38 views
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 ...
