2
votes
0answers
34 views

Specifying types of variables in pure mathematics and applied mathematics

In pure mathematics, we can write such as "an integer $a$ ..." to specify that $a$ is a given integer or $a$ runs through the ring of integers. But in contexts where mathematics is applied ...
3
votes
0answers
51 views

Etiquette for proper usage of Greek letters and other notation

I've progressed to the "output" point in my mathematics career and have run into a slightly embarrassing problem while writing a paper. Clearly, certain Greek letters are suitable for some situations ...
4
votes
1answer
109 views

How do you write an integral and why

A. Year 1 Calculus Student Approach $$ F(x) = \int f(x') dx\, $$ B. Random math paper you find online approach $$ F(x) = \int dx f(x') \, $$ C. Spivak $$ F(x) = \int f(x) \, $$ D. ??? (Edit) ...
0
votes
0answers
51 views

Alternatives to the notation $\|x\|$ for the norm of $x$?

For aesthetic reasons, I don't like the notation $\|x\|$ for the norm of $x$. Have any alternatives been proposed?
3
votes
0answers
64 views

Why not defining a measure as a function on functions?

A measure $\mu$ is a function to $\left[0,\infty\right]$ on the sets belonging to a $\sigma$-algebra. Then for integrable functions $f$ the integral $\int fd\mu$ comes in, having nice properties ...
0
votes
2answers
45 views

Which letters to use as index in sequences?

Usually the latin letters $i,j,k,l,m,n$ are used as indexes in sequences or sets with $k$ elements ($A = \{ a_1,...,a_k \} $). But when we already used all these letters is there any recommendation? ...
4
votes
2answers
120 views

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc. to represent the real number system, rational number system, natural number system respectively?
7
votes
2answers
326 views

How would you change math notation? [closed]

Mathematical notation has been evolving for hundreds of years (really thousands, I guess, but most of the noteworthy examples seem to be only a few hundred years old). Sometimes we are stuck with old ...
1
vote
0answers
49 views

Should I use the minus sign when writing papers in characteristic two

Is there any consensus regarding whether one should write both "+" and "-" or only "+" when performing computations in characteristic two fields? To give some context, I am writing my thesis, which ...
0
votes
3answers
54 views

Name of quantity that is not invariant, but only changes in one direction

How do you call a quantity that is not an invariant, but only changes in one direction during the process? Example: The degree of the polynomials go down when Euclidean division is applied, so the ...
3
votes
3answers
140 views

Do all mathematical symbols in LaTeX have a meaning?

I debated whether I should post this on the TeX forum or here. Mathematics seemed more appropriate. LaTeX has a ridiculous amount of symbols, including countless variations of the integral sign and ...
2
votes
0answers
85 views

How do we pronounce this symbol $'$ for $p',q'$, etc. And why?

This symbol $'$ for $p',q'$, etc; I know $'$, it is called prum(?) or something close to that, and $p',q'$ are p prum, q prum. But what exactly is $'$ written or pronounced? Thanks. And why is that ...
2
votes
1answer
31 views

What is the meaning of $<$ in a preorder?

Let $(P,\le)$ be a preorder, i.e. $P$ is a set and $\le$ is a relation on it that is reflexive and transitive. In this context for myself I can find two interpretations for the symbol $<$ 1) ...
1
vote
1answer
20 views

Notation for Model-Relation of formulae with free variables

Lets assume we have a formula $\mathsf{path}(x,y)$ with free variables $x,y$, and $\mathsf{acyclic}$ with no free variables on the signature $\tau = \{E\}$ (i.e. Graphs). Informally, what the formula ...
0
votes
0answers
51 views

Why is real part written first in complex numbers?

While expressing complex numbers as $a + \iota b$, is there a specific reason for writing the real part before the imaginary part? Who introduced this notation first? Is it a case where it just hung ...
0
votes
1answer
79 views

How to explain why one should use lowercase letters for variable names?

How can I explain to an Algebra I student why he should use lowercase letters when naming his variables (i.e. $q = $ number of quarters $vs.$ $Q = $ number of quarters? I am not interested in the ...
2
votes
2answers
49 views

Quick question about notation and pronunciation of indices: (i+1)st or (i+1)th?

I have a somewhat silly question: What are you calling the index after the $i$th index? The $i+1$st or the $i+1$th? How do you pronounce it and how do you write it down? I like to write $i+1$ in ...
0
votes
1answer
17 views

Pairing of Sigma and Pi in notation

Why do $ \Sigma $ and $ \Pi $ appear together so frequently in related topics. For example: Product and Sums Borel sets, such as $ \Sigma_0^1, \Pi_0^1 $ First order formulas, such as $ \Sigma_1, ...
0
votes
0answers
28 views

Standard notation for the indicator function of the odd integers

Is there a commonly used notation for the indicator function of the odd integers? One candidate I think is $$1_{2\mathbb{Z}+1}(x),$$ and I could always define one, $$\chi(x)=\left\{\begin{array}{ll} 1 ...
3
votes
1answer
94 views

What are the differences in mathematical notation around the world? [duplicate]

I just learned that $\text{sen}\,x$ is the Portuguese notation for $\sin x$, and I was inspired to ask: What differences are there in how mathematics is written around the world? Note 1: I am likely ...
0
votes
3answers
44 views

Question about variable and constant notation in some properties

I am just starting to think about mathematical notation a lot more and some parts of it do not make as much sense to me as I would like. I am operating under the convention that beginning alphabet ...
3
votes
0answers
60 views

Good confusion-avoiding notation for gluing toric varieties from fans?

$ \newcommand\R{\mathbb R} \newcommand\C{\mathbb C} \DeclareMathOperator\Cone{Cone} $I'm trying to establish a good notation to avoid confusion when we glue toric varieties from affine pieces. A ...
6
votes
1answer
65 views

Is there any advantage to the $a \equiv b\;\;(\mathrm{mod}\;c)$ notation?

Congruences modulo equivalence classes other than those defined by division remainders are ubiquitous in contemporary mathematics. It is not uncommon for a single mathematical argument to refer to ...
0
votes
1answer
32 views

Product Notation for Multiplication in Reverse Order

Is there a standard notation for multiplication in reverse order? For example consider the problem $$x_{k+1} = A_k x_k$$ where $x_i \in \mathbb{R}^n$ and $A_i \in M_n(\mathbb{R})$, ($i=0,1,2,\dots$) ...
0
votes
2answers
52 views

A question about notation

Earlier this week, a friend asked me what the most complicated equation I could think of was that was equal to $1$. The answer I gave was this: Let $G_n$ denote the n$th$ number in the grandi series, ...
0
votes
0answers
38 views

Standardizing the terminology of graph theory

I took a course in graph theory many years ago and remember being frustrated that the terminology was not at all standardized (or didn't seem to be). Various sources used vastly different words or ...
12
votes
9answers
655 views

Strangest Notation? [closed]

While this may be a fruitless pursuit of anecdotes, I still ask: what is the strangest (or most blatantly wrong (at least in the eyes of common notation)) mathematical notation you have ever seen?
9
votes
1answer
95 views

Why an integral symbol for the category of elements of a presheaf?

Let $\mathbf C$ be a category and $P \colon \mathbf C^{\rm op} \to \mathbf{Set}$ a presheaf. One can associate to $P$ the category of elements of $P$ (also called Grothendieck construction over $P$), ...
14
votes
3answers
295 views

Mathematical Notation and its importance

You can see how mathematical notation evolved during the last centuries here. I think everyone here knows that a bad notation can change an otherwise elementar problem into a difficult problem. Just ...
2
votes
1answer
52 views

Comparison of notation for sets

Different authors use different notation, no question here...but doesn't this make the study of maths a little more difficult, always chasing different definitions of how a set is represented? I ask ...
2
votes
1answer
45 views

Semidirect product notation convention

I was taught that if $G \simeq H \ltimes K$, then (by convention) $H$ is the subgroup that is normal, but I see on Wikipedia and elsewhere that other people use the convention that the above indicates ...
3
votes
2answers
68 views

Soft question: $(a_n) \in A$ or $(a_n) \subseteq A$ f0r sequences?

I have always used, in place of the full, unambiguous (but clumsy?) statement namely "Let $(a_n)_{n\geq 1}$ be a sequence where $a_n \in A$ for $n\geq 1$." the short version "Let $(a_n)_{n\geq 1} ...
1
vote
1answer
77 views

From $\mathsf{O}$ to $\mathsf{I}$ via $\infty$

The following is not true mathematics, but a little imaginary story about mathematical symbols. I wonder if there is - in parts - a true (etymological) story behind it. Once there was a symbol ...
0
votes
2answers
76 views

Nice notation for projection maps

Let $X\times Y$ be a product of two object of a category, and consider the natural projections $$ X\times Y \to X \quad\text{ and }\quad X\times Y \to Y. $$ Usually I denote them by $\pi_X$ and ...
1
vote
0answers
18 views

Good notation for many random points approximating an area.

I'm trying to say that as the number of random coordinate points points you plot approaches infinity, it is equivalent to an area integral where each point is an infinitesimally small $\mathrm{d}x ...
8
votes
4answers
207 views

Mathematical notation around the world

What are the differences in mathematical notation around the world? I know that in some other countries they write 1,2 meaning 1.2, but what else can be confusing in an academic environment (when ...
1
vote
1answer
41 views

Is it generally preferred that empty products are gotten rid of where possible?

Is it generally preferred that empty products are gotten rid of where possible? For example: Stewart's structure theorem says that for a positive integer $n$, every positive integer $\leq n$ has a ...
0
votes
2answers
27 views

Is this element-of_{ij} - looking symbol the Levi-Civita symbol?

I'm reading this formula: from a page Is the symbol that looks like an element-of symbol with two indices i and j the Levi-Civita symbol? Mathematics is my weak-side so I'm not sure. Actually I ...
2
votes
1answer
57 views

Notational Alternatives to Subsubscript

I find myself using expressions like $$a_{0_2}, (a_{n_k})_{k \in \mathbb{N}}, b_{i_{j_k}}, etc.$$ I find subsubscript and more generally, $(n \cdot \text{sub})$script for $n\geq 2$ pretty ugly and ...
1
vote
1answer
87 views

Why are Set Cardinality and Absolute Value denoted the same way?

When we have a set $A$, it is conventional to denote the cardinality of $A$ as $|A|$. When we have some number $n$, it is conventional to denote the absolute value of said number as $|n|$. My ...
0
votes
4answers
163 views

Correct formal interval notation

I can't find any definitive answer on this topic, maybe that's because there isn't one, but I figured if there was a place to ask then SE was it! To describe a set in which $x$ and $y$ are in the ...
76
votes
24answers
6k views

What are some examples of notation that really improved mathematics?

I've always felt that the concise, suggestive nature of the written language of mathematics is one of the reasons it can be so powerful. Off the top of my head I can think of a few notational ...
0
votes
1answer
50 views

We refer to X for standard notations and definitions from Y

I'm having problems with my mathematical English, so I'd like to ask for your help! Is it correct to write something like "Unless stated otherwise, we refer to [1] and [2], respectively, for standard ...
0
votes
1answer
71 views

ENS is an abbreviation of?… [duplicate]

In CWM Mac Lane uses the term $\mathbf {ENS}$ for a category having as objects the subsets of a given set and as morphisms the functions from these sets to these sets. What is abbreviated by the ...
5
votes
0answers
264 views

Paul Erdős Joke.

I was watching the great documentary "$N$ is a Number" and in it Erdős tells a joke where he writes: PGOM LD AD LD CD Which means poor great old man, living dead, archeological discovery, legally ...
1
vote
0answers
70 views

(x)f=y is more natural than y=f(x)

Has anyone ever considered the notation such as $(x)f=y$ that specifies the argument $x$ of the function first and then the function itself? I have never seen anyone use it but it seems more natural ...
3
votes
0answers
68 views

How do you type such nice solutions with all the different mathematical notation here on Math.stackexchange? [closed]

I am totally lost as to how this is done. I have never used a computer to type solutions nicely. What do I need to download? I want to learn how to type nice solutions like some of the people on this ...
0
votes
0answers
143 views

Techniques for writing mathematics and math notes so that it is more understandable to the reader using MathJax

I want to use this for my notes. Without use of colors or some indention/alignment in writing, all maths, feels like some kind of cryptic puzzle to me. I have trouble with math books, for the same ...
0
votes
2answers
50 views

How should I read this $\land$ notation?

I'm studying for SOA Exam C and I was recently introduced to this notation for a minimum $\land$. For example, if there is an limit for how much insurance can be paid out, that limit is $u$ and then ...
5
votes
4answers
332 views

Cyrillic alphabet in math

There are a lot of variables and constants in a paper that I am writing. Is any thing wrong to use Cyrillic letters for constants and Latin and Greek letters for variables? I wonder why the letters do ...