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
75 views

What does the subscript after euclidean distance notation mean?

Math noob quesetion: What does the "2" subscript mean in the picture below?
4
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1answer
54 views

How to denote the comma as an element of a set

I have a set whose elements include the comma character ",". But the comma is used as a separator when listing the elements of a set. Any suggestions for a sensible notation to use in this case?
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0answers
17 views

Is there some sort of calculus based on the notation for polynomial ring $F[x]$?

If $F$ is a field (ring), then we denote the ring of polynomials with the coefficients in $F$ as $F[x]$. This notation possesses some degree of expressiveness, e.g. I suppose we can write $F[x] \...
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0answers
17 views

The right way to formulate a minimization problem with a mix of vector and scalar

What is a right way to formulate a minimization problem that is minimizing vector $\mathbf{a}$ and scalar $b$ For example is it something like, \begin{equation} \begin{aligned} & \min\limits_{\...
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0answers
42 views

Tricky notation: Need help formulating an expression to define a recursive function involving substitutions

I'm having a difficult time trying to come up with an inductive definition for a function I'm calling $f_i(k)$ in terms of constants $\rho$, $d$, the $1 \times n$ vector $q$, and a $n \times n$ matrix ...
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3answers
102 views

Derivative Notation Explanation

I am learning differential calculus on Khan Academy, but I am uncertain of a few things. (by the way, I understand derivatives this far: $d'(x)$ and this: $d'(g(x))$) I am confused mainly about ...
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2answers
245 views

Calculator mode. ENG mode?? (SCI vs. FLO vs. ENG)

When I type 8*6 FLO = 48 SCI = $4.8 * 10^1$ ENG = $48 * 10^0$ 1) What is the point of ENG mode?? 2) What are situations where you want answers in SCIentific notation?
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2answers
26 views

Significant figures: Trailing Zeros in Scientific Notation.

I'm wondering how you determine the number of significant figures of a number in scientific notation with trailing zeros. For example: $3100.0*10^2$ (which is not in correct scientific notation) ...
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2answers
76 views

How to solve $(k-\sqrt{k^2-4y^2})- 10sin^2((m -y)/5)= 0$ and how to embed the solution of equations in other formulas

I have a formula like this $5-\sqrt{25 -4 x^2}$, and I know that the value of $x$ is the solution to a rather complicated equation $$(k-\sqrt{k^2-4y^2})- 10sin^2((m -y)/5)= 0 $$ The (only) solution ...
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1answer
26 views

A question on notation and a particular step in the analysis of Apollonius Prop 108

I am studying an analysis of the following lemma: "Given a circle and two points D, E within it, to draw straight lines thought D, E to a point A on the circumference in such a way that, if they meet ...
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1answer
100 views

What does $\operatorname{supp}(A)$ mean?

I'm looking at a paper (specifically this one). In the paper, we have a positive operator $A$, and the operator $\operatorname{supp}(A)$ is supposed to be a projection operator. Does anybody know ...
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4answers
72 views

How do you denote the opposite of a range of numbers?

What I want to do, is find the conventional standard to denote a range of numbers not included in a set, which is itself part of an infinate set. For e.g: A range of numbers, from say, -∞ to 0, and ...
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1answer
100 views

Tensor notation for 3-D matrix expression

I have the expression $y_i = \displaystyle\sum_j x_j \!\cdot\!a_{ij} \!\cdot\! \exp \Big(\sum_k b_{ijk} \!\cdot\! x_k \Big)$ which I want to shorten without introducing more notation than necessary. ...
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1answer
32 views

Propositional logic notation by problem solving

I'm having a hard time understanding some propositional logic notation in the following problem: Given the formula $F = (¬p ∧ ¬q) ∨ (p ∧ ¬q)$, define the formula's truth value $A_{B}(F)$ by ...
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1answer
27 views

General question regarding constants and variables

I'm currently doing work on discrete mathematics in my free time and am having some difficulties with understanding some questions pertaining to relations and functions. To be specific, I'm stuck on ...
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0answers
15 views

How to represent a set of conjunctively connected predicates

I have set of predicates $P=\{p_1,p_2,...,p_n\}$, now from this set I need another set, lets name it $P'$. Basically, $P'$ should contain all elements of $P$ connected conjunctively. Is this a correct ...
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0answers
117 views

Summation Notation and Iverson Bracket

I was looking for summation notation with conditional sum. Mathematical notation for a conditional sum referred about Iverson Notation. Is this equation correct using summation and Iverson notation? ...
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0answers
6 views

Is there a custom way to mark faulty digits of approximations?

To quantify how bad an estimation is, we can compute its relative error. I would like to visualize it by marking the faulty digits: is there a customary notation to do so ?
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2answers
84 views

How widely known are Iverson brackets?

Here on the Mathematics Stack Exchange I recently learned about the Iverson bracket notation: $[P] = \begin{cases} 1 & \text{if } P \text{ is true;} \\ 0 & \text{otherwise} \end{cases}$ It ...
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0answers
65 views

What does the notation $\langle x^n:\; x\in G\rangle$ mean?

If $G$ is a group, what does $$G^n:=\langle x^n:\; x\in G\rangle$$ for a fixed $n\in\mathbb{N}$ mean? This should be a subgroup of $G$ but I din't know the definition of $\langle x^n:\; x\in G\rangle$,...
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1answer
33 views

Sum for all element of the sum of x for every element

Let $i$ be an element of the set $S$. Suppose that you need to calculate a sum of many rates $\rho$ for every element $i$, and then the sum these sums for all elements of the set $S$. How do I write ...
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1answer
73 views

Is there an encyclopedia of mathematical notation?

For example - for set complements, it would include all common notations such as 'A - B' or 'A \ B'
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1answer
47 views

What does a limit sign with a line either top or bottom mean?

Can someone please explain what the symbols $\varliminf$ and $\varlimsup$ mean?
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2answers
74 views

Which notation is wise to consdier?

Consider that $f(x)$ is a continuous function on the closed interval $\left[ a,b \right]$. Also, its $n$-th derivative is continuous on $\left( a,b \right)$ where $n$ is any desired integer. I mean ...
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1answer
28 views

Single variable calculus: confusion about directional derivative

I am stuck on deriving proving the following equalities: given $x,y,t$ scalar and $f$ a scalar function (1) $\lim\limits_{t \to 0} \dfrac{f(x + t(y-x)) - f(x)}{t} = \left.\dfrac{df}{dt}\right|_{t \to ...
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0answers
38 views

Defining a singleton in $[0, 1]$

I have seen a singleton in the [0,1] set defined as: $\{b\}=\bigcap\limits_{n=1}^{\infty}(b-1/n, b+1/n] \,\cap\,\Omega$ I am trying to learn some set theory in connection to the need for probability ...
2
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1answer
66 views

Does $\sin(2x)^2 = \sin(2x^2)$ or $(\sin(2x))^2$

In the notation $\sin(x)^2 $ Does this equal $\sin(x^2) $ or $(\sin(x))^2 $ ? I'm sorry this is such a simple question but Google is unhelpful. There are plenty of sources illustrating $\sin^2(x) $ =...
2
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1answer
38 views

“standard co-deviation”

This is a terminology/notation question. I swear I've seen covariance matrices written as \begin{bmatrix} \sigma_x^2 & \sigma_{x,y}^2 \\ \sigma_{y,x}^2 & \sigma_y^2 \end{bmatrix} Given ...
2
votes
1answer
53 views

A monoid where every element has finitely many divisors

Is there a special name or has there been any study of monoids of this form? This came up in considering the general construction of a multivariate power series algebra over a ring $R$; usually we ...
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0answers
36 views

How to interpret the gradient of a vector field, rather than a scalar field,

If $\vec u(y,t)$ is a mapping from $R^{n+1}$ to $R^n$, then I can write out the n component functions of U, each as a function from $R^{n+1}$ to $R$ $$\vec u(y,t)=(u_1(y_1,...,y_n,t), ... ,u_n(y_1, ....
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0answers
19 views

What is $|k|_3$?

I'm reading the 2003 Recurrence Sequences and trying to figure out notation related to S-units. It does not appear earlier in the section (or the book, as far as I can tell) and doesn't appear in the ...
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2answers
111 views

Is this weird “such that” notation valid? [closed]

I've seen that the phrase "such that" can be notated as a $|$ or a $:$, specially when you are using a set builder notation. My Geometry teacher also occasionally uses an $\in$ but "backwards" when ...
1
vote
1answer
98 views

Subvector matrix notation

Is there any notation indicating a subvector of a matrix ? I need to know the correct way of showing it in an academic paper. i.e: Let $$ A=\begin{bmatrix} 2& -10 & 0 & 4\\ 5& ...
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2answers
62 views

What is difference between notations a|b and a/b?

I am just a beginner. Can somebody tell me what is the exact difference between these notation, if any? $a|b$ and a/b
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2answers
18 views

A question about Game Theory Notation in symmetric Games

In Martin Osbourne and Ariel Rubenstien's book A Course In Game Theory (page 20) the authors say that a 2 person game is symmetric the A1 = A2 (both players have access to the same action set) and (...
0
votes
1answer
54 views

What is the correct (i.e., precise) term for a vector of the form $(a_1,…,a_n)$?

What is the correct (i.e., precise) term for a vector of the form $(a_1,...,a_n)$? I ask this because my definition of vector is that it is an element of some vector space, this means that whenever ...
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0answers
34 views

Are choice function and axiom of choice equivalent?

Axiom - True for all $X:$ if $X \neq \emptyset,$ then there's some $f: X \to \cup X$ such that for any $A \in X, f(A) \in A.$ But the axiom above looks very much like the choice function. Are they ...
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1answer
46 views

question about Einstein summation

why is this expression valid? $ c_{i}(x_{i}+y_{i}) $ it has the index repeated 3 times instead of 2 times.
2
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1answer
66 views

Notation for the set $\{1,2,..,k\}$

I often find myself using the set $\{1,2,..,k\}$, sometimes on multiple occasions in a sentence. I've been told that $[k]$ is a short notation for this, but have never seen that in use. Could someone ...
1
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0answers
30 views

In math notation, how to indicate that one number is supposed to be appended/prepended to (or inserted in) another number as a whole?

I don't know if there exists a special, separate term for this operation in mathematics (maybe "to ascribe"?), but here is an example. Let's say I have a variable $m=2$ and I want to write it at the ...
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2answers
132 views

First Order Logic Question - “All cats either love or hate dogs.”

Given the following set of predicates: $$\{cat(x), dog(x), love(x, y), hate(x, y)\}$$ How would you transform the following English statement into First Order Logic... Statement: "All cats either ...
3
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0answers
93 views

Tensor notation generally

I'm pretty new to tensors in differential geometry and I have a basic question about the notation used. In general a vector field $X$ can be expressed as $$X=\sum_{i=1}^n X^i \partial_i,$$ where $X^...
0
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1answer
51 views

What is the notation for a system of simultaneous equations?

Both in school and university, systems of simultaneous equations were denoted by a straight line in front of the equations (like a determinant, but no line after). Now I find out that both LaTeX and ...
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0answers
16 views

Matrix language and notation confusion

"Matrix M is row indexed by all elements of [v] and column indexed by selected k-subsets of [v]" What does row/column indexed mean in this statement. What does [v] mean ie what does [] represent?
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0answers
10 views

End behavior of the intersection of 1-e^{-2x} and 2sin^2 (x)

Graphing the two graphs, there are many solutions (because of the sins). And I wanted to see what the intersections approached. So I tried taking the end limits of both sides: $$lim[1-e^{-2x}]=lim[...
0
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1answer
32 views

About fibers and bijection

If $T = \{q\}$ consists of a single element of $B$, $f^{−1}(T)$ is called the fiber of $f$ over $q$. Thus a function $f : A \to B$ is a bijection if it has nonempty fibers over all elements of $B$ (...
2
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2answers
103 views

Indicator function notation

Which of the following is correct: $$t \mapsto t\textbf{1}_B(t)$$ or $$ t \mapsto t\textbf{1}_B$$ for some set $B$? Here $\textbf{1}$ denotes the indicator function, and the function I am trying to ...
0
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0answers
14 views

Autoconvolution Notation

Is there any special notation for a list (or function) convolved with itself? For example, the convolution of the list [1,1,1,1] with itself produces a new list: [1, 1, 1, 1] * [1, 1, 1, 1] = [1,...
3
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1answer
69 views

Mathematical Symbols

I'm working on a constructed language that borrows concepts from existing languages. Does anyone know if there is a consolidated set of universal symbols out there? I looked at Wikipedia and I noticed ...
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2answers
112 views

Can you assume midpoints in geometry? [closed]

When you have a diagram such that line segment VY has a point X that looks like it is in the middle of the segment, but the question doesn't state that, can you assume that X is the midpoint of ...