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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408 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, ...
5
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1answer
84 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
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1answer
447 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
43 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
47 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 common/...
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0answers
51 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
232 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
87 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
63 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 ...
3
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1answer
84 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
40 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
106 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
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1answer
63 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
97 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
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2answers
279 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, $\bf{V}^...
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0answers
126 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 as:...
2
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2answers
113 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: "...
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2answers
185 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
37 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 Y=\left\{(x,y)...
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1answer
208 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 $\max(x, 0)$?
-1
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1answer
52 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
65 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 ...
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1answer
62 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 ...
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4answers
108 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?
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2answers
55 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
35 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 ...
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1answer
46 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 ...
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2answers
64 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
77 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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1answer
34 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
79 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.
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1answer
104 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 ...
2
votes
1answer
77 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.
1
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0answers
75 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
34 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 ...
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5answers
72 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
32 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] = \{5,0,1,2,3\}...
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0answers
93 views

Standard notation for the set of children of a node in a rooted tree

In graph theory, given a rooted tree $T$ and a node $a \in V(T)$, is there a standard way to refer to the set of all children of $a$? I have seen $CHILDREN_T(a)$ being used, but this seem quite clumsy ...
1
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1answer
64 views

How to express double orthogonal complement?

Let $V$ be a Hilbert space and $U \subseteq V$. Then $U^\perp = \{\mathbf{v} \in V|\forall \mathbf{u} \in U, \langle \mathbf{u}, \mathbf{v} \rangle = 0 \}$. My question is, how do you express $\left(...
0
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0answers
40 views

What does this matrix notation mean?

What does $|\textbf{M}|$ mean, where $\textbf{M}$ is a matrix? I am under the impression that you can element-wise divide $\textbf{M}$ by $|\textbf{M}|$ to normalize it in some way, kind of like how $|...
3
votes
1answer
66 views

What is the proper use of Leibniz notation for one-sided derivatives?

The only notation I've seen has been restricted to either Lagrange's prime notation or Euler's $D$. Here are some of the variants: $$f'(a^+):=\lim_{x\to a^+}\frac{f(x)-f(a)}{x-a}$$ $$D_+f(x):=\lim_{h\...
2
votes
1answer
76 views

What does $\Bbb R/2\pi$ for a set mean?

I simply cannot figure out what this means. I read this on an article about the scalar product of $2\pi$ periodic functions. it says that < f,g > goes from $\Bbb R/2\pi \to \Bbb C$ (complex) Do ...
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1answer
949 views

Can ∂x and ∂y in a derivate be seen as ∂ times x or ∂ times y?

I'm watching some tutorials on machine learning and know just enough calculus to have an intuition on what a derivative is, but that's it. But this question is bugging me so much that now I'm pretty ...
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0answers
54 views

Set Theory Notation: What does it mean to “\” one set with another? [duplicate]

What does the "\" operator mean in the above context?
3
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7answers
174 views

The meaning of the symbol $\infty$ in Spivak's calculus book

Spivak in "Calculus" writes ... symbols of $\infty$ and $- \infty$ are purely suggestive: there is no number $``\infty"$ which satisfies $\infty \geq a$ for all numbers $a$. What is the meaning ...
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1answer
60 views

In the expression $p^2=4q_1$, what does the small $1$ mean?

In the image below there is $p^2 = 4q$ and then a small $1$. What is the name/meaning of this notation? I have never seen it before and can't find what the meaning of it is. Help is appreciated! See ...
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1answer
29 views

Notation question $|X^2|$

I am studying a little bit of set theory, and one of the questions in the book (in Efe A. Ok's real analysis book) asked to show that $\dim(X,\succeq)\leq |X^2|$, where $X$ is a finite set and $(X,\...
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1answer
66 views

Is there a short symbol that denotes integration?

I want to illustrate partial integration, see below. With derivatives we can just write $(term)'$. Is there something similar for integration? The best I could come up with is $\int(term)\mathrm{d}x$. ...
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0answers
40 views

What does a * mean after a letter signaling a result?

I have this equation from a biology publication. It's about an ecosystem model. $$\frac{df}{dt}=w(f)f(1-f)-vf$$ $w(f)$ is a function and $vf$ is a multiplication. Then what does $f^*=0$ or $f^*>0$...
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1answer
138 views

Meaning of “$\triangledown$u*ñ=0 on the boundary”

I'm doing homework for my PDE class, I'm coming across this notation and I don't what the ñ means: $\triangledown$u* ñ=0. I have tried to google it, but unfortunately questions like this don't really ...