0
votes
3answers
31 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
43 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
62 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
21 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
49 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
34 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
579 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?
14
votes
3answers
236 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
48 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
35 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
63 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
69 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
16 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
167 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
25 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
49 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
61 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
115 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 ...
72
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
43 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
59 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
213 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
66 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
117 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
46 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
238 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 ...
2
votes
0answers
71 views

Symbol for functions that vanish on boundary?

If I have a domain $ M \subset \mathbb{R}^n $, is there a standard symbol for the set of functions $ f \in C^\infty(M) $ that vanish on $ \partial M$ ? I feel like I have seen this before, but I'm ...
6
votes
2answers
197 views

The notations change as we grow up

In school life we were taught that $<$ and $>$ are strict inequalities while $\ge$ and $\le$ aren't. We were also taught that $\subset$ was strict containment but. $\subseteq$ wasn't. My ...
13
votes
3answers
240 views

Working with subsets, as opposed to elements.

Especially in algebraic contexts, we can often work with subsets, as opposed to elements. For instance, in a ring we can define $$A+B = \{a+b\mid a \in A, b \in B\},\quad -A = \{-a\mid a \in A\}$$ ...
3
votes
2answers
78 views

A question on notation for open sets

Yesterday I was presenting a seminar where I started using this notation to make sentences shorter; whenever I wanted to say that $A$ was open in $B$, I would write $A\underset{op}\subset B$, with the ...
6
votes
1answer
223 views

Is there a rigorous theory of context, whereby sets can gain additional structure within a context?

Consider sets $G$ and $H$ and a function $f : G \rightarrow H$. So far, it doesn't really make sense to ask whether $G$ and $H$ are groups (technically, the answer is "no, they're not groups"), and ...
4
votes
0answers
82 views

Why is the Euclidean metric called the prime at infinity?

I've been studying p-adic analysis recently and after a bit of searching on the web, I haven't found an answer as to why the Euclidean metric is referred to as the 'prime at infinity', and given the ...
4
votes
4answers
612 views

Sequence Notation — Which brackets to use?

I'm teaching sequences at the moment. I've always put sequences in round brackets, for example $(1,2,3,4,5)$ is a sequence whose first member is $1$, whose second member is $2$, and so on. I've also ...
1
vote
6answers
162 views

Super or subscript notation on the left hand side of a symbol?

Are there any commonly used notations with super or subscripts on the left hand side of the symbol? or on both sides of a symbol? If so, then what is the latex for having sup/sub script on left or ...
2
votes
2answers
66 views

Why is $S/R$ a ring extension?

If $S$ is a ring and $R \subset S$ is a subring it's common to write that $S/R$ is an extension of rings. I frequently find myself writing this and read it quite often in textbooks and lecture notes. ...
10
votes
2answers
469 views

Is there a collection of alternative mathematical notation? (Semi-soft Question)

I'm interested in alternative systems of notation for mathematics. I've often heard how mathematical notation is illogical, inconsistent, filled with grandfather clauses that serve no purpose, and ...
13
votes
2answers
310 views

The double factorial notation

The double factorial is defined as $$n!! = \begin{cases} n \cdot (n-2) \cdot (n-4) \cdots 3 \cdot 1 = \dfrac{(n+1)!}{2^{(n+1)/2}((n+1)/2)!} & \text{ If $n \in \mathbb{Z}^+$, is odd}\\ n \cdot ...
14
votes
2answers
628 views

The Gamma function and the Pi function

I have been studying differential equation, in particular special functions. Euler's Gamma function, and Gauss's Pi function are essentially the same, differing only by an offset of one unit. for ...
41
votes
7answers
3k views

Why is 'abuse of notation' tolerated?

I've personally tripped up on a few concepts that came down to an abuse of notation, and I've read of plenty more on stack exchange. It seems to all be forgiven with a wave of the hand. Why do we ...
1
vote
2answers
129 views

What does means the $\frown$ in sequence notation?

In the theorem 3.6 of Juhász's Cardinal Functions in General Topology appears the following symbol about sequence: $\frown$ The role context of it's appearance is the following: Theorem. Let X be an ...
2
votes
2answers
822 views

Is there a Math symbol that means “associated”

I am looking for a Math symbol that means "associated" and I don't mean "associated" as something as complicated as isomorphism or anything super fancy. I am looking for a symbol that means ...
4
votes
5answers
621 views

Why do mathematicians use this symbol $\mathbb R$ to represent the real numbers?

So, I'm wondering why mathematicians use the symbols like $\mathbb R$, $\mathbb Z$, etc... to represent the real and integers number for instance. I thought that's because these sets are a kind of ...
7
votes
1answer
599 views

Why use radical notation instead of rational exponents?

I'm helping my younger sister for her math class. She has recently been taught integer exponents, and has starteed studying radicals (mainly square roots). The next topic will be rational exponents, ...
7
votes
1answer
135 views

When do modifiers denote sub or super? Pseudo-, quasi-, ultra-, strong-, well-, pre-, c0- …

One only needs to search MMA.SE, math journals, wikipedia, or god-forbid, n-cat lab, for keywords listed in the title, which can be extended with: uniform-, regular-, complete-, local-, partial-, non- ...
9
votes
1answer
174 views

Articles on ideas in the history of mathematics notation?

I'm teaching a course this term on the history of scripts (writing systems) and rather than talking interminably about Semitic and Chinese and their spawn, I'd like to give students a more varied ...
2
votes
3answers
228 views

Is there a reasoning behind the depiction of the numbers as they are $\{1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9\}$?

Is there a reasoning behind the depiction of the numbers as they are: $$\{1,2,3,4,5,6,7,8,9\}$$ Is there any other form of depiction for $6$ and $9$ other than $VI$ and $IX$?
4
votes
4answers
157 views

Why Does Finitely Generated Mean A Different Thing For Algebras?

I've always wondered why finitely generated modules are of form $$M=Ra_1+\dots+Ra_n$$ while finitely generated algebras have form $$R=k[a_1,\dots, a_n]$$ and finite algebras have form ...