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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3
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4answers
127 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
23 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
24 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
86 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
65 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
88 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
35 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
41 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
20 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
61 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
42 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
66 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
21 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
30 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
40 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
31 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
54 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
272 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
21 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
62 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
176 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
46 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
96 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 ...
1
vote
2answers
336 views

Linear Algebra Done Right Example 1.7

In the book Linear Algebra Done Right I came across this example for the sum of vector spaces. Did he say the second $W + U$ is still equal to 1.7 because it doesn't matter whether you say $(x+y, ...
4
votes
1answer
68 views

What is the set $\mathbb{R}^{\nvDash}$ defined as?

The set $\mathbb{R}^{\nvDash}$ is used in my multivariable-calculus assignment, but I do not know what the superscript '$\nvDash$' means on the set of real numbers. The context in which it used is ...
7
votes
1answer
407 views

Integral notation for degree homomorphism on algebraic cycles

In Fulton's Intersection Theory, he develops the notation $\int_X$ for the degree homomorphism from $A^*(X)$ to $\mathbb{Z}$, and I was wondering if there was a reason for the notation. Is this in any ...
0
votes
1answer
21 views

Show that the conditional probability $P(\cdot | C)$ satisfies the axioms of probability, and is thus, indeed, a probability function.

The Statement of the Problem: For a fixed event $C$ such that $P(C) \gt 0$, show that the conditional probability $P(\cdot | C)$ satisfies the axioms of probability, and is thus, indeed, a ...
4
votes
1answer
41 views

Notation: Set where function is positive

Given some function $f: X \to \mathbb{R}$ from some space $X$ to the reals. I have sometimes seen the notation $\{f > 0\}$ used to denote the set $\{x \in X : f(x) > 0 \}$. Is this a ...
1
vote
0answers
22 views

Use of vinculum to indicate a group of variables represents digits of a number

In my country, there's a long-standing tradition of using the vinculum in contexts similar to this: Let $\overline{ab}$ be a two-digit natural number. Show that ... I have only happened once to ...
1
vote
4answers
218 views

$\{∅\} ∈ \{∅\}$ is this right or wrong?

I am very confused about whether $\{∅\} ∈ \{∅\}$ or not. I thought it's right because in curly brackets the phy is also a member. Can anyone help me understand this?
-1
votes
4answers
81 views

Is $\log^22^k = (\log2^k)^2$?

Does the square of $\log^22^k$ include whole $2^k$? Is $\log^22^k = (\log2^k)^2 = \log2^k \cdot \log2^k = k^2$? The base of my $\log$ is $2$.
0
votes
0answers
40 views

Confused about Graph Theory Language

I was confused about some of the wording in this definition I came upon: Let G be a control flow graph (a control flow graph you can imagine as a directed graph) for program P. A hammock H is an ...
0
votes
1answer
36 views

Standard notation for brackets around trigonometric arguments

I've been going through this site quite a lot lately and I've noticed one thing, the notation $\sin(x), \, \cos(x), \, \tan(x),\ldots \,$ is used frequently. Now, I do tend to bracket the arguments ...
3
votes
1answer
49 views

Set Notation with exponent

I am looking at the function: $$f: \{5\}^2 \to \{5\}$$ it is certainly nothing too exceptional , but I find it difficult to understand what $\{5\}^2$ as a set notation and from then the whole ...
0
votes
0answers
32 views

Separability in Algebra and Topology

I am wondering about the use of the word separablity in two different areas of mathematics, namely algebra and topology. In topology, we call a topological space $(X,\mathscr{T})$ if it contains a ...
2
votes
1answer
47 views

What do these symbols mean in equations 4 and 5 on this page?

I'm looking at an old math textbook on the Internet Archive. On page 17 of this pdf at the bottom it has 2 formulas. One has what looks like an apostrophe and the other has a dot (like a ...
0
votes
1answer
43 views

Notation: determinant of Jacobian matrix

Given a function $f:\Delta^n \to Y$ from a simplex into a riemmannian manifold. Furthermore given a point $x \in \Delta^n$ we can send an orthonormal basis at $x$ using $D_x f$ to a set of vectors ...
2
votes
2answers
34 views

Help understanding Product (capital PI) notation

On the wikipedia article for lagrange interpolation (https://en.wikipedia.org/wiki/Lagrange_polynomial), it shows the definition for the lagrange basis functions in a strange way - well strange to me ...
3
votes
2answers
45 views

What is the bar symbol over a complex scalar in the expression $\overline{\lambda}$?

I have the following problem from section 1.4 (Vector Spaces) of Peter Peterson's Linear Algebra textbook. I am having trouble with the way multiplication is defined on the given vector space, ...
1
vote
0answers
37 views

Bach Tensor Definition and Notation

I encountered the following in a paper (http://arxiv.org/pdf/math/0310302v3.pdf) and I'm hoping someone could confirm my interpretation of it. The paper defines the Bach Tensor in local coordinates ...
2
votes
2answers
89 views

Set theory formula

I picked up a copy of Jech's Set Theory at my school library and I'm reading through it and taking notes. Right at the beginning, though, he mentions something called a 'formula'. Here's the quote: ...
0
votes
2answers
42 views

What is the meaning of the notation of function

More specifically, what is meant by the function $T: \mathbf V \to \mathbf W$? I saw it in the discussion of linear map in Axler's Linear Algebra Done Right but could not understand this notation. ...
1
vote
2answers
36 views

If $A$ is a set and $\mathcal B$ is a set of sets, is there some shorthand for $\left\{A\times B:B\in\mathcal B\right\}$?

Let $A$ be a set and $\mathcal B$ be a set of sets. Suppose we want to define $$M:=\left\{A\times B:B\in\mathcal B\right\}\;.$$ Is there some shorthand for $M$ as we've got for $$X\times ...
0
votes
1answer
44 views

Is there a mathematical operator to truncate negative values to zero?

Is there a mathematical symbol that truncates a value x to 0 if it is negative, and leaves it untouched otherwise? Something which is logically equivalent to $\max(x, 0)$?
0
votes
1answer
33 views

Notation in Munkres' Elements of Algebraic Topology

What is $ R^{N} $ in section 1 of chapter 1 of the book Elements of Algebraic Topology by J.R. Munkres? Is $ N $ some natural number?
0
votes
2answers
46 views

What is the difference between $x \bmod y$ and $x \pmod y$?

I'm currently taking calculus I. So I'm new with is all notation, and looking through the Internet I always thought $x \bmod 3$ means the remainder when you divide $x$ by $3$. Am I wrong, and is ...
0
votes
1answer
30 views

Symbol to denote length of geometric vector

I have seen both $\left|\vec{u}\right|$ and $\left\|\vec{u}\right\|$ when referring to the Euclidean length of a geometric vector $\vec{u}$. Which notation is preferred. Is it true that the latter ...
0
votes
4answers
100 views

What is the function “mod”

Surfing this site, I have often seen many functions and expressions involving $\bmod$ and I have no clue about its meaning. What does that $\bmod$ mean?