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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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
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1answer
27 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
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0answers
37 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: ...
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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
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2answers
53 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
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5answers
268 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 ...
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0answers
20 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 ...
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3answers
60 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?
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3answers
173 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 ...
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1answer
42 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
95 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 ...
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2answers
332 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
66 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
399 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
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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
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1answer
40 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 ...
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0answers
20 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 ...
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4answers
212 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?
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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 $2$.
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0answers
38 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 ...
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1answer
31 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
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1answer
47 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 ...
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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 ...
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1answer
45 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 ...
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1answer
39 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
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2answers
31 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
36 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, ...
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0answers
30 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 ...
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2answers
79 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
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2answers
39 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. ...
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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
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1answer
40 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
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1answer
32 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?
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2answers
45 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
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1answer
26 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
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4answers
97 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?
0
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1answer
35 views

Trouble Understanding Notation in Reinforcement Learning Paper

I'm looking at this (warning: this is a download of a pdf) paper and am having trouble parsing the notation on top of page 11, steps 4.1 and 4.2. $\forall i \leq t \in T$, $\forall$ $x_i$, $a_i$ ...
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1answer
30 views

Query description into mathematical notation

I need to formalize two query descriptions into mathematical notation. The source of this description, if anyone is interested in broader context. Query 1: Frequent routes The goal of the query ...
0
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1answer
35 views

How to evaluate this combination of sums and integrals?

I am reading a book on PDEs, and I am near the beginning where the author is talking about the heat equation and, specifically, solving the non-homogenous equation $u_t={\alpha}^2u_{xx}+f(x,t).$ The ...
2
votes
2answers
44 views

What is the correct way to write this matrix equation?

Given an $n \times m$ matrix $X$ and $m \times m$ matrix $A$, I would like to define the vector $y$ as $$y_i = X_{i,*} A (X_{i,*})^T$$ where $X_{i,*}$ is the $i$th row of $X$. Is there a simpler ...
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0answers
26 views

Given a matrix M, is there a name for the matrix MM^T?

One can make a symmetric square matrix out of any m-by-n matrix $M$ by computing the matrix $MM^T$ (or $M^T M$). Is there a name for this operation? I want to call it "symmetrizing" the matrix, but I ...
0
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0answers
20 views

Vector in vector notation

I'm a bit confused as far as notationally differentiating between row and column vectors goes. Suppose I define a column vector $$\boldsymbol{a} = (a_{1}, a_{2})^{T}$$ and another column vector ...
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2answers
49 views

What does $A^{B}$ mean? [duplicate]

Assume, that A and B are finite sets. What notion $$A^{B}$$ does mean? Have been looking for awhile now.
1
vote
1answer
58 views

What are the meanings of the various turnstiles

It is easy to find the meanings of $\vdash$ and $\models$ (see this question and Wikipedia) but what of the (triple?) turnstile $\Vvdash$ and the (vertical double?) turnstile $\Vdash$? Do they have a ...
0
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1answer
49 views

What do these group theory notations mean: $\overline{3}\otimes\overline{2}$, $\overline{2}\oplus\overline{3}$

Can you explain or give a good reference to explain notations like $$\Large\overline{3}\otimes\overline{2}\qquad\qquad \overline{2}\oplus\overline{3}$$ and combinations of these. Thank you.
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0answers
34 views

Notation in probability theory: conditional on multiple events or joint of event with an conditional one

It might be a quite dumb question and if so, I apologize in advance (I am kind of a newbie in probability theory ). But once in a while it bothers me and I can't find the answer to it. Ok, now the ...
0
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1answer
21 views

Notation for a projection of a differential form

Let $\omega = a_1 dx_1 + a_2 dx_2 + b_1 dy_1 + b_2 dy_2$. Is there any established notation to denote a mapping that "filters out" the $dy_i$-Terms? To be more precise, I invent my own one. Assume ...
0
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5answers
65 views

Is there any notation for general $n$-th root $r$ such that $r^n=x$?

As we know that the notation for the $n$-th principal root is $\sqrt[n]{x}$ or $x^{1/n}$. But the principal root is not always the only possible root, e.g. for even $n$ and positive $x$ the principal ...
0
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1answer
20 views

Intervals of integers modulo n

Do the following related concepts appear anywhere in literature? Denoting an "interval" in the integers modulo $n$ by $[i,j] = \{i, i+1, \dotsc, j\}$. For example, in modulo 6, $[5,3] = ...