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.

learn more… | top users | synonyms

0
votes
0answers
44 views

Formulation: Smooth vs. finitely often differentiable

I treat the cases $f\in C^\infty$ and $f\in C^k$ in different sections of my thesis. While I am happy with the title smooth functions for the first section, I am not so sure if finitely often ...
0
votes
2answers
90 views

How to denote an even number in mathematics? [closed]

I need a sign for an even number (not $a\cdot 2$) in my formula. I tried to google it, but I saw only $2a$. Please tell me if there is a special sign?
1
vote
1answer
59 views

Inserting parentheses to produce different values

Without grouping symbols, the expression $$\verb/2 ⋅ 3 ^ 3 + 4/$$ has a value of $58$. Insert grouping symbols in the expression $\verb/2 ⋅ 3 ^ 3 + 4/$ to produce the indicated values. ...
0
votes
1answer
23 views

Notation for polynomials and equating coefficients

I am reading a paper that defines $P_k(s|t)$ as a polynomial of degree $k$ in $s$ given $t$. Does this mean that each term is of the form $f_{k}(t)s^{k}$? (What does "given $t$" mean?) The paper ...
0
votes
2answers
71 views

What's the meaning of the $R(f(x),g(x))$ in $\int R(f(x),g(x))?$

Usually when I'm reading about integration, there is a notation for integrals on some forms, for example: $$\int R(\sin(x),\cos(x)) \;dx$$ Obviously I've deduced that this represents functions that ...
9
votes
3answers
878 views

Must all Lebesgue integrable functions really be invertible?

I am studying Lebesgue integration after a course on Riemann integration, and the definition of measurable function is given as follows: $f:{\mathbb R}\rightarrow {\mathbb R}$ is measurable if the ...
2
votes
2answers
48 views

Is there accepted notation for the pushforward measure that doesn't mention $\mathbf{P}$?

Let $(\Omega,\mathcal{F},\mathbf{P})$ denote a probability space, $(S,\mathcal{M})$ denote a measurable space, and $X : (\Omega,\mathcal{F},\mathbf{P}) \rightarrow (S,\mathcal{M})$ denote a measurable ...
1
vote
1answer
335 views

How to calculate a posterior probability with a given Gaussian Mixture Model?

I'm building a GMM-based classifier in speech processing and I'm using GMM as a probabilistic scoring mechanism (therefore I don't intrinsically care about the underlying mixture components). For ...
1
vote
1answer
166 views

Should I use set notation or list notation when writing out a basis of vectors?

I think in Sheldon Axler's Linear Algebra Done Right, he makes a comment about why the technically correct way is to write vectors in lists, such as $(v_1, ... v_n)$, while many books use set ...
2
votes
1answer
772 views

How do I determine the domain and range of the following relations using set builder notation?

I have been given the following relations to find the domain and range of using builder notation. (The blue writing is what I have so far) I am just beginning to learn the whole concept of set ...
0
votes
0answers
60 views

What does $D^n$ refer to?

I'm not sure what object $D^n$ is in the following exercise: "Write down an explicit homeomorphism between $D^n/S^{n-1}$ and $S^n$." Thanks!
0
votes
3answers
221 views

Why do mathematicians use $\oplus$ instead of $+$?

What is the historical reason for using $\oplus$ instead of $+$ to denote operations that are generally thought of as addition? Similarly, why is $\otimes$ used instead of $\times$ (or just $\cdot$) ...
22
votes
12answers
4k views

What do sine, tan, cos actually mean?

I know that $\sin\theta=\frac{y}{r}$ and $\cos\theta=\frac{x}{r}$. My question is: is $\sin$ a function of $\theta$, as in $\sin (\theta$)? If yes, why is there no $\theta$ on the right hand side of ...
0
votes
3answers
62 views

What does P|a means?

In the proof for the existence of unlimited prime numbers, i saw the following let n be the number of prime numbers as P1,P2,P3,.......Pn let a = P1P2P3....Pn+1 a > Pn and a is not a prime number a ...
1
vote
3answers
33 views

Set numbering representation

I want to represent proper element of sets. For example, $$ A=\{1,2,3,4\} $$ $$A(2)=2$$ But I wonder that this expression is right. Because I know that the set has not order. How can I do this??
4
votes
2answers
72 views

Notation of an infinite union

Is there any difference between: $$ \bigcup_{n =1}^\infty a_{n} \\ \bigcup_{n \in \mathbb{N}} a_{n} $$ From my understanding they both define an infinite union. Is this correct?
0
votes
1answer
17 views

Operator for comparing an n-tuple

Suppose you have to compare the following two finite ordered list of elements (tuples): $(\psi_{i}, R_{i}, A_{i}, \eta_{i})$ and $(\psi_{i}^{*}, R_{i}, A_{i}, \eta_{i})$ and for instance it turns out ...
1
vote
1answer
12 views

Name for map associated with simplicial complex

Given a simplicial complex $\Delta$, implied by the construction process there are associated maps sending euclidean standard simplices into the simplicial complex $\imath: \Delta^n \to \Delta$. What ...
1
vote
1answer
45 views

Interpretation - exponential loss formula

i stumbled upon the following formula while studying the concept of exponential loss. I try to understand this formula. I read it as follows: The function that minimizes the expected exponential loss ...
0
votes
1answer
45 views

What is usually understood as DOMAIN and CODOMAIN of a Relation

Suppose I have a relation declaration as $R \subseteq A \times B$, such that $A=\{1,2,3,4\}$ and $B=\{10,20,30,40\}$. And suppose that the definition of this relation is $R=\{(1,20),(3,40)\}$ We ...
0
votes
1answer
129 views

Four mathematical notations for fraction $1/999$ and how to show/present they are equal

I need some help for notation. I need to present fractions in four different format and I'd like to get it right. I just take $1/999$ for example, but of course it could be any fraction with positive ...
14
votes
6answers
966 views

Notation of the differential operator

I see the differential operator both with upright and italic d in different books/articles. So I'm curious about $$ \int x^2 \, dx \quad \text{vs.} \quad \int x^2\, \mathrm{d}x,$$ and ...
1
vote
1answer
38 views

Matrix,Linear algebra,polynomial,finite field,notation

In the book by Arora and Barak,Computational Complexity,on page 168,1st paragraph, there is a notation which I do not understand. They write For every $n \times n$ matrix $A$,and $i\in [n]$,we define ...
-3
votes
1answer
57 views

What does it mean by a function $ f(x)=\exp(O(|x|^2)) $ for $|x|$ large?

Given $f(x)$ is continuous in $(-\infty,\infty)$ and $ f(x)=\exp(O(|x|^2)) $ for $|x|$ large. Now I have an I expression like ...
2
votes
2answers
100 views

What is the symbol to denote that two triangles are similar?

Does there exist a unique symbol to denote that two triangles are similar to each other without resorting to using the phrase "is similar"?
3
votes
4answers
147 views

How to notate all integers $\gt 1$ except products of $2, 3 , 5$?

What is a notation for all whole numbers greater than $6$ which are not a product of $2, 3 , 5$? $7$ would the first, then $11, 13, \ldots$ also $7\times 7$ or $11\times 11$ would be included. As a ...
2
votes
1answer
27 views

Notation - matrix calculatoin

i am self-studying linear algebra, and came across the following statement about singular value decomposition (X = $USV^T$). I am somewhat confused on how to interpret the (|) and (--) symbols. Should ...
0
votes
1answer
29 views

Notation for matrix that is partially unknown.

I have a matrix with some elements known and some unknown. I am using the notation $A(X)$ where $X$ are the unknown elements (not sure if relevant but I will be solving for the unknown part $X$ ...
3
votes
2answers
105 views

Notation for Tautologies

I've been stuck for a while in this question and so far I don't understand the flaw of my reasoning please if you guys could help me out. See, this is my context. From the definition of argument we ...
0
votes
2answers
79 views

Meaning of symbols like $\inf\limits_{\epsilon>0}$

I am very confused at the precise definition of the following symbols. A reference or explanation would be great. $$\Large\inf\limits_{\epsilon>0}\qquad \sup\limits_{\epsilon>0}$$
1
vote
4answers
94 views

Difference between $f(x(t))$ and $f(t,x)$

Why is there a difference between the two differential equations: $\overset{.}{x}(t)=f(x(t))$ and $\overset{.}{x}(t)=f(t,x)$ ?
0
votes
0answers
42 views

Succinct notation for specifying that eigenvalues must have negative real part?

Is there a succinct way to denote that all eigenvalues of a matrix $A$ have negative real parts? If the eigenvalues were real, I could simply write this as $$-1 < A < +1$$ since we have the ...
2
votes
0answers
51 views

Riemannian Geometry notational tricks or alternatives

I am interested in learning tricks that people have developed to speed up / clean up calculations in Riemannian Geometry. I am hopeful about this question because there is often a lot of symmetry in ...
1
vote
1answer
21 views

Is this true: $\frac{f(x)}{1-c-o(1)}= \frac{f(x)}{1-c}(1-o(1))$

Let $f$ be a function, for example $f(x)=log(1+x)$ and let $c$ be some constant $>0$ (for simplicity, we may assume that it is different from 1). Is this true: $$\frac{f(x)}{1-c-o(1)}= ...
3
votes
1answer
32 views

Name for a nonlinear version of bilinear form

A map $b:X \times Y \to \mathbb{R}$ is called a bilinear form if $b$ is linear in both arguments. Is there a name for a form $b$ which is linear in only one argument and may be nonlinear in the ...
0
votes
2answers
66 views

A Series might be a number or a sequence – Is there a better notation?!

Take the expression $\sum_{k=1}^\infty a_k$. Sometimes this expressions refers to the sequence of partial sums $\left(\sum_{k=1}^n a_k\right)_{n\in\mathbb N}$ and sometimes to the limit of this ...
2
votes
1answer
63 views

Succinctly writing some code in vector/mathematical notation - how?

I’m trying to learn how to correctly represent some code I have in vector notation. Apologies if it’s a bit convoluted, keep in mind I’m trying to learn how to better communicate it (!) The code ...
1
vote
1answer
67 views

What groups are that? What does : mean?

What are the groups 2^6 : 3 . S_6 or 2^4 : A_8 ? Are they some subgroups of S_6 or A_8? I believe that 2 . A_n is the double cover of A_n, and "multiplying" with a number gives a covering group. But ...
0
votes
1answer
22 views

Representing a combinatorial sum with an equation

I am trying to represent a situation with an equation that is fairly conceptually simple, but I am not sure what is the proper way to represent it as a formal mathematical equation. I have a set of n ...
1
vote
1answer
57 views

E Scientific Exponential Notation

Gday, I have a question regarding scientific notation. Today I learnt that $a\operatorname{\mathbf{E}}b$ is the same as $a\cdot10^b$ and since myself and examiners (I'm in year 12) like neat working ...
2
votes
0answers
48 views

Proper names for different representations of the same formula

I would like to know what to call formulas that are all on one line and what to call the same formulas that are on multiple lines. One line example: P ÷ TVD ÷ 0.052 Multiple line example: ...
0
votes
0answers
40 views

In a chain of equalities/inequalities, is each line referring to the previous one?

In a chain of equalities/inequalities, or equalities/containments: $$\begin{align*} A & = B\\ & \subsetneq C\\ & = D \end{align*}$$ to which element is the last part refering to? In ...
2
votes
2answers
58 views

Notation - “' sign” in summation

I am studying logistic regression - and i saw the following symbol: c' (in sum symbol of the denominator). What does this mean? I thought it might be all other elements of the vector except the one ...
12
votes
5answers
286 views

Is $1 : 7 = 1 / 8$ or is it $1/7$?

In a certain (non-mathematical) Stack Exchange, when I wrote $n : m = n / m$ where $n$ and $m$ are positive integers, one of the moderators said "No! $n : m$ is usually the notation for "$n$ parts in ...
0
votes
0answers
30 views

Notation for “set of leaves of a tree” when leaves are “repeated”

Having this tree, I need to specify the number of leaves (6) and the set of leaves. Question: is this the correct notation to specify the set of leaves when there are some repeated or is there ...
-2
votes
3answers
78 views

Logic notation question

If I have some statements $P$ and $Q$ and I have the following logic formula: "$P$ or $Q$", does that mean only one of them is true or both of them can be true?
4
votes
3answers
216 views

Typesetting the mathematical expression “const.”

How do I write in the right way, that something is constant? I think, usually one does write = const., which should be an abbreviation for the Latin ...
1
vote
1answer
84 views

what is the handwritten notation for a random vector?

Not sure if this is a maths question but didn't know where to turn. I'm learning probability theory on my own using a textbook. It uses capital letters with subscripted number to denote random ...
3
votes
1answer
44 views

What's Being Returned Here?

I'm working my way through this paper, and I'm having a bit of trouble understanding what it's telling me to do. Here's the specific excerpt that's tripping me up: A (finite) one-shot game is a tuple ...
2
votes
3answers
142 views

Is there any difference between 'all real numbers' and '$(-\infty, \infty)$'

I've just thought about this. All the textbooks I've been looking at for pre-calc, the domains are always written as 'all real numbers', whereas my calculus textbooks would rather write them as ...