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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70 views

Notation question: Superscript on brackets around a set with a metric

Simplifying a bit, I encountered this notation: Where $\cal M$ and $\cal N$ are sets, each with a metric, $[{\cal M}]^{4\epsilon} \supset [{\cal N}]^{3\epsilon}$ . Any guesses as to the meaning of ...
3
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2answers
41 views

Notation for indexing an indexed sequence.

I have a notation question. Say I have the following: $S = \{a_{1}, \ldots, a_{n}\}$ a finite list of integers (order matters). What I really want is to express that now I pick only $K$ elements, in ...
4
votes
3answers
98 views

What does $]a,b[$ mean? [duplicate]

I recently encountered the above notation for sets, and I've never encountered it before. What does it refer to?
0
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1answer
55 views

Is it common to notate a probability density function with Pr(..)?

My understanding is - and my internet-research reassured me - that one uses lower-case letters for the probability density function and upper-case letters for absolute probabilities. 'p' vs 'Pr' for ...
0
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1answer
75 views

What's FORMAL Logic Notation? Logic Inference Problem too

Is this a proper example of FORMAL logic notation? (Ǝ c ∈ Cookies such that Ǝ d ∈ duck, d wants c) I have a question that requires an answer in 'formal' logic notation. I'm assuming that they're ...
2
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0answers
59 views

Multiple composition of function notation

Let's say I have a set of $n$ functions of $m$ variables: $$f_1(x_1,x_2,\ldots,x_m),f_2(x_1,x_2,\ldots,x_m),\ldots,f_n(x_1,x_2,\ldots,x_m)$$ Is there a notation that represents $(f_1 \circ f_2 \circ ...
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votes
4answers
123 views

What does the symbol $+: E\times E$ mean in $+: E\times E\to E$?

What exactly does the symbol, $ +: E\times E$ mean in the formula $+: E\times E\to E$? In other word why such a symbol/operation is used to represent addition in the vector space?
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1answer
104 views

Name of symbol of null set.

What is the name of the symbol we use for empty set? Difference in notation of phi and void set? I found that symbols that we use for both are different but I know the name phi only. Not know the name ...
2
votes
1answer
43 views

Notation regarding integral w.r.t. a measure

While reading articles about statistical inference and SMC algorithms I have come by the following notation (never seen in school) to represent the expectation w.r.t. a measure $\mu$ $$ \mathbb{E}[\...
3
votes
2answers
30 views

In an interval notation answer, are you supposed to put a space between the two terms or not?

For example, if the answer is [-1, ∞) should you write it like that or like this [-1,∞). Does it make a difference?
-1
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3answers
76 views

Comparison (<, >, …) notation for sets

Are comparison notations such as <, >, ≤, ≥, =, ≠ valid for sets? I'm interested in stating size (number of elements) relations between sets.
2
votes
1answer
80 views

Uniform norm $ \|u\|_{C(\overline{U})}$ in PDE

Let $U\subset \Bbb{R}^n\to\Bbb{R}$ be an open set (not necessarily bounded) and $u:U\to\Bbb{R}$ be a bounded continuous function. In Evans's PDE textbook, the author defines a norm $$ \|u\|_{C(\...
1
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1answer
42 views

Notation of One-Sided Limits

If we had $\lim\limits_{x\,\rightarrow\,a^+} f(x)$, would the notation $\lim\limits_{x\,\downarrow\,a}$ be exactly the same as $\lim\limits_{x\,\rightarrow\,a^+}$, or is $\lim\limits_{x\,\rightarrow\,...
2
votes
2answers
34 views

Question about notation in Wolfram's “Composition of series with power and logarithm”

In this Wolfram webpage, under the section "For compositions with elementary functions" they give the following identities: Power functions: Log+power functions: However, in those equations, ...
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0answers
47 views

Numerical Mathematics and Computing - 6 digit rounding arithmetic

This is a homework problem on a mathwebsite (webwork) which states: For the function f(x)=sqrt(x+4)−2, find an alternative formula that can accurately evaluate its value for small x. To which I ...
2
votes
1answer
390 views

What does “arg inf” mean?

I noticed this term on this post. But the term arg inf is not clearly defined.
3
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1answer
39 views

How would I interpret this function notation?

$y=f(x)\Leftrightarrow x^2 y+y=7$ How do I go about even reading this, let alone solving this? I also have to find the domain of "$f$"
0
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0answers
24 views

Splitting summation over natural numbers

I have this slight problem of how to split the summation notation over natural numbers. That is, for $n \in \mathbb{N}$, $\mathbb{N}$ = {1, 2, 3, ...}, $$\sum_{j=1}^{\infty}a_j = \sum_{j=1}^{n-1}a_j +...
3
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1answer
765 views

Does this operator exist already?

Is there any pre-established operator or function that is zero if any of its operands is zero, otherwise negative if any of its operands is negative, otherwise positive? The sign is the most ...
0
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4answers
64 views

Math Piecewise style, which one is correct/best?

I am writing my Computer Science Master Thesis. I am wondering what is the correct or in your opinion best looking style for piecewises: See examples below: Do I use a comma at the end of each line ...
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1answer
69 views

Why $i^2=-1$ in complex numbers? [closed]

Why do we use specifically iota (where $i^2=-1$) in complex numbers? Complex numbers are used in multi-dimensional applications. But we can also use any symbolic term in place of $i$. Why do we use ...
0
votes
2answers
35 views

notation: mapping $f\rightarrow\int_{0}^{1}f$ of $C(I)$ to $\mathbb{R}$

Can anyone explain what the following notation refers to: mapping $f\rightarrow\int_{0}^{1}f$ of $C(I)$ to $\mathbb{R}$ This is from a question asking about uniform continuity of $f$ on $C(I)$, but ...
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0answers
49 views

Covariant Derivative Along Arbitrary Vector

The inspiration for this question is section 1.3 of "A Course in Minimal Surfaces," by Colding and Minicozzi. This section has to do with deriving the first variation formula. We are dealing with an $...
0
votes
2answers
64 views

What does the sum notation $\sum\limits_{j=n}^\infty a_j$ mean?

What does the sum notation $\sum\limits_{j=n}^\infty a_j$, $n\in\mathbb{N}$, mean? Is this the sequence of the sums, i.e: $$ \sum_{j=n}^\infty a_j=\left( \sum_{j=1}^\infty a_j,\; \sum_{j=2}^\...
3
votes
1answer
44 views

How do I solve this kind of sigma notation problem?

How do I solve the following? (by hand, its easy to find an answer with a calculator but I need an answer than can be done with some kind of rule/formula/identity). $$\sum_{n=1}^5 n^n$$ and is there ...
1
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1answer
64 views

I need help verifying the answers to these exercises [Velleman, Chapter 1.1, Q5]

I've begun to study Daniel Velleman's "How to Prove It" and I need to clarify a few things and ensure I've gotten the answers correct before I move on. I've questions about quite a few of the ...
6
votes
2answers
152 views

What does the sum notation $\lim_{n\to\infty} \sum_{j=n}^\infty a_j$ mean?

What does the sum notation$$\lim_{n\to\infty} \sum_{j=n}^\infty a_j$$ mean? Is the $n$ fixed or not?
1
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2answers
98 views

$\mathbb{R}^\ast$, $\mathbb{R}_+$, $\mathbb{R}^\ast_+$ “deprecated”?

I have recently stumbled upon this page in ProofWiki, which asserts that the notations $$ \mathbb{R}^\ast = \mathbb{R}\setminus \{0\} $$ and $$ \mathbb{R}_+ = \{x\in\mathbb{R} \mid x\geq 0\} $$ are ...
0
votes
3answers
99 views

Short notation for intervals of real and natural numbers

Are there short, common, and intuitive notations for intervals of real and natural numbers that explicitly use $\mathbb R$ and $\mathbb N$ as basis of their notation? The main purpose of the notation ...
0
votes
1answer
58 views

On the mathematical convention used to talk about biconditional proofs

Given $P \Longleftrightarrow Q$, the following does apply: $P \Rightarrow Q$ is equivalent to: $P$ is a sufficient condition for $Q$, $Q$ is a necessary condition for $P$. $Q \Rightarrow P$ is ...
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0answers
23 views

Question about the notation

I was studying linear algebra with the Kostrikin's book when I found this notation: $$f(e_1,\cdots,e_n)=(f(e_1),\cdots,f(e_n))=(e'_1,\cdots,e'_n)A_f$$ But I couldn't understand what it means, once ...
0
votes
2answers
41 views

Confusion in symbols of a book

I was reading book "" Concrete Mathematics by Ronald L. Graham AT&T Bell Laboratories, ] Donald E. Knuth Stanford University, Oren Patashnik Center for Communications Research"" and I cam across ...
0
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1answer
32 views

Covariant derivative notation?

I was reading up on covariant derivatives and came across this document. On the second page it says: We define a procedure called parallel transport by defining a vector $\vec A (\lambda)$ along ...
0
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2answers
48 views

Mathmatical notation of random function

A function $f$ projecting from $\mathbb N$ to $\mathbb N $ is denoted as $f: \mathbb N \rightarrow \mathbb N$. I is OK to denote the common random() function, i.e., without input parameters, as it is ...
0
votes
0answers
19 views

Increasing/decreasing notation

I've seen the following notation being used when someone is talking about right-continuous functions: $$\lim_{x \rightarrow x_0^+} F_X(x) = F_X(x_0),$$ $$\lim_{x \downarrow x_0} F_X(x) = F_X(x_0).$$ ...
0
votes
1answer
30 views

Shorter notation for $\{1,…,N\}$ and $\{-N,…,N\}$

Often I need to write something like $n \in \{1,...,N\}$ or $n \in \{-N,...,N\}$ in subscripts and sums. I'd like to use something a bit shorter. Looking around at all the notation questions on Math....
1
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2answers
69 views

What is the difference between $-1^2$ and $(-1)^2$? [duplicate]

Intuitively, I though that $-1^2$ and $(-1)^2$ were exactly the same thing; however, it seems I was wrong as Wolfram Alpha (and any other calculator) returns $-1$ for the first case and $+1$ for the ...
1
vote
1answer
113 views

What conventions surround the meaning of expressions like $\int \frac{1}{x} dx$?

I really struggle with the notation $\int f(x) dx$ because of the whole $+\,C$ thing, and this becomes double pronounced when $f(x)$ isn't defined everywhere. For example, we learned in high school ...
3
votes
1answer
37 views

Unknown notation used in matrix proof.

I have been given the following task (by my professor, with no mentionable context): Prove that $\displaystyle \left[ \begin{array}{rr} a_{11} & a_{12} \\ a_{21} & a_{22} \\ \end{array} \...
0
votes
0answers
43 views

Convergence notation in measure theory

In Olav Kallenberg's Foundations of Modern Probability he uses $\uparrow$ and $\rightarrow$ to express two seemingly different types of convergence. Let $0 \leq f_1 \leq f_2 \leq $ be a sequence of ...
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1answer
31 views

What does $\mathrm{M}_{2}(\mathbb{F}_{7})$ mean in terms of matrix fields

I just need to know what exactly this means
4
votes
1answer
24 views

Question about notation for Hermitian metrics on complex manifods

The standard notation for a Hermitian metric looks like this: $$\sum ds^2 = \sum dz_i \otimes d\overline{z_j}.$$ The conjugate confused me for a while until I explained it to myself as follows. In ...
0
votes
0answers
30 views

Making sense of an Expected Utility of a Mixed-strategy Profile definition

I came across a definition of Expected Utility of a Mixed-strategy Profile in Brown's and Shoham's "Essentials of Game Theory: A Concise, Multidisciplinary Introduction" where: "Given a normal-form ...
0
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1answer
34 views

Space of smooth functions with compact support.

Quick question regarding the generally accepted definition for a space. Suppose we consider the space $C_{0}^{\infty}(\Omega)$ of smooth functions of with compact support in $\Omega$, do we ...
2
votes
2answers
112 views

What does the notation $C(\bar U)$ mean for $U\subset\Bbb{R}^d$ open?

Let $U$ be an open subset of $\Bbb{R}^d$. In Evans's PDE book, $$ C(U)=\{u: U\to\Bbb{R} \mid u\ \hbox{continuous}\} $$ and $$ C(\bar U)=\{u\in C(U)\mid u\ \hbox{ is uniformly continuous on bounded ...
2
votes
1answer
60 views

Notation of $\partial$

What are concepts that are generally notated by $\partial$? I know two things that are denoted by $\partial$. Those are "the boundary of a set in a topological space" and "partial derivatives". What ...
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1answer
34 views

Intersection of a closure

What is the intersection of a closure? That is, $U$ is a open set, then what is:
3
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3answers
57 views

Difference between $(-x)^{1/n}$ and $-x^{1/n}$?

I know these seems to be splitting hairs, but according to two different calculators, there's a real difference. For e.g, $(-8)^{1/3}$ computes to NaN, where $-8^{1/3}$ computes to $-2$. Though am ...
0
votes
3answers
83 views

Notation for derivatives: $u_{xx}$ versus $u''$

If I have a problem in which I'm supposed to find $u(x)$ such that $u_{xx}(x) - 3u_x(x) + 2u(x) = 0$, is the equation the same as $u(x)''-3u(x)'+ 2u(x) = 0$, meaning that the first term, $u_{xx}(x)$, ...
2
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2answers
78 views

Does the notation $r^3\propto t^2$ mean the same as $t^2\propto r^3$?

I was recently reading about Kepler's third law of planetary motion. There in two books I saw two different things. In one place it is written $r^3\propto t^2$ and in the other book it as written $t^2\...