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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2
votes
1answer
50 views

Implementing the $\Rightarrow \Leftarrow$ contradiction symbol?

How is the $\Rightarrow \Leftarrow$ symbol actually used in practice? I think my issue here is that I don't know what the symbol is meant to mean. For example, I know that $\implies$ means "which ...
3
votes
2answers
57 views

what does $[0,1]^\omega$ mean

The question is, Give $[0,1]^\omega$ the uniform topology, find an infinite subset of this space that has no limit point. I just want to know what does $[0,1]^\omega$ mean so I can proceed. I'd ...
6
votes
2answers
102 views

What does this notation mean: $\mathbb{Z}_2$

$\mathbb Z$ (Our usual notation for the integers) with a little subscript at the bottom. This is the question being asked: what are the subgroups of order $4$ of $\mathbb Z_2 \times\mathbb Z_4$ ...
6
votes
0answers
95 views

Why use Einstein Summation Notation?

Einstein summation convention dictates that repeated indices should be summed. Thus the equation $a_{ij} = b_{ik}c_{kj}$ is taken to mean $a_{ij} = \sum_k b_{ik}c_{kj}$ where in both cases the range ...
1
vote
0answers
20 views

Denoting bijection (conjugation) in a commutative diagram

I have a simple notation question: I there a standard way how to denote in a commutative diagram that a map is a conjugation? I thought of the following three, but: The left one (simple arrow) ...
0
votes
0answers
23 views

When to use $argmin$ and $Argmin$?

What is the difference between the notations $argmin$ and $Argmin$ precisely? If I'm not mistaken one is used when the set of points attaining a minimum of a function has more than one point and the ...
0
votes
0answers
26 views

Mathematical (and any other related e. g. statistical/economic…) Notation System

I would like to ask where I could find really extensive source (websites, books, whatever you are aware of) for studying purposes in terms of mathematical notations. This is really a must for me, ...
0
votes
1answer
42 views

What this notation R^3 ∖ (0, 0, 0) means?

I was reading a "Projective Space" article on Wikipedia, when I came across this line "equivalent definition is the set of equivalence classes of $\mathbb R^3 \setminus (0, 0, 0),$ i.e. 3-space ...
0
votes
0answers
13 views

The definition of $C(\bar U)$.

In 'Partial differential equations, Evans', $C(\bar U)$ is defined by the space of continuous functions $u\in C(U)$ such that $U$ is uniformly continuous on bounded subsets of $U$. But I have known ...
4
votes
1answer
53 views

Why is the notation $f=f(x)$ mathematically correct?

Looking at the equation, which is written all over my textbooks, $f=f(x)$ or $\mathbf r = \mathbf r(x,y,z)$ or what-have-you, I can't help but think that that is just wrong. On the LHS is a function. ...
1
vote
2answers
63 views

“for almost all” symbol

Is there a standard symbol for “for all but finitely many”? I had a professor who used to make an inverted capital lambda crossed by a little concave arc. And I found it in Super-recursive ...
6
votes
2answers
39 views

Is there any convenient notation for a vector entry j at iteration step i?

I have a stupid question: I'm writing a master thesis and I have to describe an iterative method of an algorithm. The method uses vectors which are manipulated at each iteration step. Now my ...
0
votes
1answer
16 views

Notation for disjoint inequalities

Is there a standard notation for representing disjoint inequalities? For example, let's say that I have an equation that may be solved under the following conditions: $ x \leq a$ OR $ x \geq a+b$ is ...
0
votes
1answer
29 views

Correct notation for “slice” of Integers

Say I want to have the set of all integers between any two given integers $a$ and $b$. For example, if I want the set of all integers between $-3$ and $7$ I would get: $$ \{-3,-2,-1,0,1,2,3,4,5,6,7\} ...
0
votes
0answers
54 views

How to present set of point in mathematical way

I have a question about presenting the set of point in the math. I have two sets in domain $\Omega$. $M$ is set of $m$ point locations, $N$ is set of $n$ point locations. In which,some points in the ...
0
votes
2answers
18 views

Is there any difference between those two notations of a quantum state?

In "Quantum Computing verstehen", the author uses both $|ab>$ and $|a,b>$ to describe the state of a 2-bit quantum register. Is there any important difference between those two notations or do ...
0
votes
0answers
19 views

Notation for image and kernel capitalization of first letter

In the mathematical notation for image and kernel one usually writes $\ker$ for kernel and $\DeclareMathOperator{\img}{Im}\img$ for image. Why is the "k" small but the "I" big?
1
vote
0answers
26 views

Notation $\mathrm{mod} $ in ergodic theory

Does someone know, what exactly is meant by the following: $$T^{-1}A=A \mod \mu$$ where $\mu$ is a $T$-invariant measure?
0
votes
1answer
20 views

Representing textual solution to problem using Math notation

If I person $A$ & $B$ both have $40$ dollars, how much must $A$ give $B$ so that B has $10$ dollars more that $A$? Answer is $5$ dollars. $A$ now has $35$ dollars while $B$ has $4$5 dollars. How ...
4
votes
4answers
132 views

Why can you not omit the '*' sign for multiplication in Sage, Matlab, and other mathematical software?

Question I have some experience with Sage and Matlab. Both mathematical software packages require you to have the '*' sign when multiplying symbolic variables with integers. For example, in Matlab ...
2
votes
1answer
58 views

What does $E^{\mathbb{C}}$ mean?

I was reading a book (Symplectic Geometry and Quantum Mechanics) and find it hard to understand this following example: Definition: a "complex structure" on a vector space $E$ is any linear ...
1
vote
1answer
29 views

Slice, projection, contour: A terminology question.

Consider a multivariate function, say $y=f(x_1,x_2,\dots,x_n)$, and suppose that $z=f(x_1,x_2,\dots,x_{n-1},g(x_1,x_2,\dots,x_{n-1}))$. What do we call $z$ with respect to $y$? Projection, level set, ...
0
votes
1answer
40 views

Mathematical notation: sorting nonzero elements in a matrix

I have a set $X = \{X_1,\ldots,X_n\}$ where $X_i = [x_1,\ldots,x_m]$ and $x_k$ can be any positive integer value including zero. I want another set $Y$ such that only the values of $X$ that are ...
1
vote
0answers
52 views

What's the definition of $x^g$?

My question is really simple. I'm studying a book of group rings which doesn't define what is $x^g$, where $x,g$ are elements of the group $G$: Thanks
1
vote
2answers
31 views

Meaning of notation $v \mapsto ( x \mapsto f(x,v) )$

I came across this notation in this wiki article. Can anyone tell me the meaning of this notation? What exactly is happening here? $v \mapsto ( x \mapsto f(x,v) )$ What I understand here is $x, v ...
4
votes
2answers
36 views

Should I use different parenthesis in calculations?

I was taught in a school that one should denote the order of computations by different brackets like $2\cdot \{3+[2\cdot (8+9)]\}$ Do the teachers taught me wrong as for example the notation $\{\}$ ...
1
vote
1answer
24 views

how to express finite set of finite sequences

I want to define a finite set of finite sequences and they may have distinct cardinality. Is it correct to express this as follows: Let $S=\{x_{n_{i}}: n=0,1,...,m \quad \text{and} \quad ...
7
votes
1answer
94 views

What came first, the $\forall$ or the $\exists$? [closed]

I imagine that these symbols originated in one of the following ways: "I will declare a symbol for "for all." I will just use the letter "A" flipped upside-down. Yes, let $\forall$ represent "for ...
1
vote
2answers
32 views

Curious about some (basic?) linear algebra notation

I was reading an old linear algebra textbook today, and I was actually having some trouble understanding the notation given in a problem. Here is what it said (or something similar): Consider the $n ...
5
votes
3answers
89 views

Integration with $d($“some function”$)$ instead of $d($“some variable”$)$.

$$\int x\,d(x^2)=\;?$$ I am confused with this. Usually we have $d($"some variable"$)$, not $d($"some function"$)$. My attempt is the following: $$\int x\,d(x^2)=\int ...
16
votes
5answers
3k views

How many digits does the integer zero have?

Should zero be classified as having no digits, or 1 digit?
1
vote
4answers
69 views

How to represent sign function in range $[-1, 1]$

I have a function that is defined as follows: $$f(x) = \begin{cases} 1 & \text{if $x \ge0$}, \\ -1 & \text{if $x<0$}. \end{cases}$$ I would like to represent the above function by the ...
0
votes
3answers
70 views

Formal notation for representing decimal numbers

What is the formal mathematical notation for representing a decimal number using variables as it's digits? I am honestly surprised that this has not been asked yet on MSE. Let me clarify a ...
2
votes
1answer
41 views

Writing an expression as a product of products

I am currently dealing with the following expression: $$\left(\prod_{i=1}^{N-1}(\lambda_N-\lambda_i)\right)\left(\prod_{i=1}^{N-2}(\lambda_{N-1}-\lambda_i)\right)\cdots (\lambda_2-\lambda_1)$$ Is ...
5
votes
4answers
88 views

What does $\Bbb{C}(X)$ refer to?

I have from a book (b) Let $E = \Bbb{C}(X)$. Then $\operatorname{Aut}(E / \Bbb{C})$ consists of the maps $X \mapsto \dfrac{aX + b}{cX + d}, ad-bc \neq 0\ldots$ Not sure what $\Bbb{C}(X)$ is. ...
4
votes
5answers
118 views

Why is $\sqrt [n] 1$ not an expression “in radicals” of a root of unity?

In Edwards' Galois Theory, in the chapter on Cyclotomic polynomials, the author devotes a lot of effort to proving that prime order primitive roots of unity can be expressed "by radicals", and gives ...
2
votes
3answers
36 views

Sigma Notation For Indexing Over Non-Consecutive Integers

My Question: How do I know by which number to increase my adding from start to finish with Sigma As far as I have learned when using sigma with a rule from start and finish your number always ...
0
votes
0answers
63 views

Unknown notation

I have a notation that looks like this: $(\pi(915..917))$ what would the interpretation of this be? I would like to get it to be an arithmetic progression but I'm not sure. Is there any other ...
2
votes
1answer
23 views

Meaning of the mapping

I am reading basic sets. In the section of sesquilinear mapping, I came across this mapping $f: X \to X^*$ i.e $x \ $ maps to $ (x|.)$ Here I know $X$ is a function space, I guess $X^*$ stands ...
2
votes
0answers
30 views

Simplification that I don't understand

There's this following rewrite that I don't get. I have little to no experience with $o$'s and $\epsilon(x)s$ other than basic knowledge from a definition. $$(o((x-a)^n) = ...
0
votes
0answers
25 views

Translation of GENUS to Portuguese

Does somebody know a translation (to portuguese) for "genus" in topology? Theorem: A nonsigular projective curve in $\mathbb{P}_2$ is topologically a sphere with $g$ handles. Definition: This number ...
3
votes
0answers
54 views

$\times$ as symbol for multiplication, how common is this?

I never encountered the $\times$ symbol denoting multiplication (of real numbers or real-valued functions) since middle school until I found it recently in the measure theory notes by D H Fremlin. ...
-1
votes
1answer
25 views

Dirac Delta Function definition with ksi (ξ)

The dirac delta function has a definition $$f(0)=\int_∞^∞f(x)δ(x)dx$$ and $$ f(x)=\int_∞^∞f(x-ξ)δ(ξ)dξ $$ (the lower bound is minus infinity but I couldn't add a minus :/) I do understand the ...
1
vote
1answer
27 views

Derivative of $\ f (y/x)$

I had a little argument with a friend about this. Let $f$ be a differentiable function such that $$g(x,y,z) =xy \ f \left( \frac{y}{x} \right) -z $$ Then, is it mathematically correct to write (I ...
0
votes
0answers
17 views

Notation for powers of a limit?

Perhaps this belongs in the TeX SE over here, but I was trying to find the conventional notation for taking a limit to a power. e.g. for the square of the limit of $f(x)$ as x approaches a, is ...
4
votes
4answers
281 views

The caret ^ symbol means exponentiation informally in math. Why not a symbol for log too? [closed]

Plus, minus, multiply, divide, and exponentiation all have symbols in math (+, -, *, /, ^ ) . But why isn't there the missing log symbol too? Here's how it would work: 4 ^ 5 = 1024 (as is standard ...
9
votes
1answer
95 views

Is the pushforward measure a categorical-theoretic pushout?

Given two measurable spaces $(X,\mathscr{F}),(Y,\mathscr{G}),$ $f:X \to Y$ measurable and $\mu:\mathscr{F} \to [0,\infty)$ a measure, the pushforward of $f_*(\mu):\mathscr{G} \to [0, \infty)$ is ...
0
votes
1answer
44 views

What does $|\langle A,B \rangle|$ mean?

I was wondering what $|\langle A,B \rangle|$ mean, where both are vectors, if I am correct. Thanks!
1
vote
1answer
38 views

Notation of field extensions and ring extensions

For example the notation for rings like the Gaussian integers uses brackets: $\mathbb{Z}[i]$. Yet the notation for field extensions uses parentheses, like in the case of the Gaussian rationals ...
0
votes
1answer
20 views

Converting prime notation of derivatives to Leibniz notation.Resources needed

I have been studying calculus for past few months and through the time I have been using the so called prime notation.I have been studying from Spivaks Calculus for those of you who are familiar with ...