Use the convention tag for questions about standard, cultural practices in mathematics.

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17
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7answers
2k views

Why do we (mostly) restrict ourselves to Latin and Greek symbols?

99% of variables, constants, etc. that I run into are named for either a Latin character (like $x$) or a Greek character (e.g. $\pi$). Sometimes I twitch a little when I have to keep two separate ...
2
votes
1answer
28 views

Is there an agreed upon convention for naming ZFC+Large Cardinal Axioms?

Is there an agreed upon convention in general for what to name ZFC+[Large Cardinal Axiom]? Or would one have to state explicitly which axiom was being added? To explain what I mean, note that anyone ...
0
votes
0answers
19 views

Limit Terminology

From the $\epsilon-\delta$ definition of a limit, we can see that any limit can be broken up into two "one-sided limits". These "one-sided" limits are simple cases that arise as a consequence of the ...
1
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0answers
35 views

Product of Cycles: Name to denote “direction” of composition

Is there a notation to denote the difference between these two products of cycles? It seems as though there are two conventions out there that should have a specific name for them. The subscripts for ...
1
vote
2answers
18 views

Convention - Dual $\pm$ Signs

Say I have two equations like $$z+w=x+y$$ $$z-w=x-y$$ Is there any way I can combine these into a statement like $$z\pm w=x\pm y$$ I know the above statement is not correct as that entails 4 different ...
1
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1answer
16 views

Analogue of right-inverse for non-surjective function

Given a function $f: X \to Y$, not necessarily surjective, is there a common name (and more concise definition than follows) for a function which maps elements in $Y$ where $f$ is defined to elements ...
1
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2answers
26 views

Global decimal mark use

Is it feasible that one convention will be decided on with regard to the use of a decimal comma or decimal point and similarly, thousand separators? i.e. 1.000 vs 1,000
1
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1answer
18 views

A question about convention of writing identities and formulas

I'm only a third year undergraduate math student, but I've seen a decent amount of formulas, identities, and equations (at least enough to formulate such a question). However, I haven't actually ...
1
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2answers
21 views

Symbolic denotation of the space of all eigenvectors

There is a symbolic notation for the set of all eigenvalues $$\operatorname{spec} \varphi = \lbrace \lambda \in K \mid \lambda \textrm{ is an eigenvalue} \rbrace$$ There is also a notation for the ...
1
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0answers
18 views

Distribution functions: differentials in the numerator or denominator

One paper I'm looking at says, $n(M, z) \, dM \, dz$, the number of sources with mass $M$ at a redshift $z$, in the mass interval $dM$ occurring in the redshift interval $dz$. While another ...
0
votes
1answer
26 views

A Summation Convention – Substitution Rule

I'm new to this forum. I'm starting a PhD – it's going to be a big long journey through the jungle that is CFD. I would like to arm myself with some tools before entering. The machete is Cartesian ...
1
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1answer
78 views

Is there an open / established categorization / list of terms / concepts and synonyms for mathematics?

I am currently thinking about how to bundle some of the efforts of students to get / create good educational material. One idea of this little project (wiki-ed - still in the very early phase) is to ...
1
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2answers
48 views

How would this combinatorial process be written in conventional mathematical notation?

Now, I am going to define an operation on a list of numbers, which I will treat as a set, for want of a better approach. This may not be ideal, or even conventional, so apologies for lack of clarity ...
1
vote
1answer
61 views

Is there an analog of $\epsilon$ in complex analysis?

When someone writes let $\epsilon > 0$ in the context of calculus, we know the intention is that $\epsilon$ is real, and may be made as small as we like. Is there a corresponding symbol (Greek ...
4
votes
2answers
627 views

Convention of digit grouping after decimal point

I read that different cultures have different ways of grouping digits before the decimal point for readability e.g. 1234567890 can be grouped as 1 234 567 890 (English), 12 3456 7890 (Chinese) or 1 23 ...
12
votes
5answers
514 views

Why are the order-of-operations conventions good?

Children are sometimes taught silly mnemonics like "PEMDAS" to remember conventions on order of operations. (I never heard of "PEMDAS" until long after graduating from college, as far as I can ...
3
votes
0answers
72 views

Handwriting cardinal numbers [closed]

In books the cardinal numbers are usually written with a gothic font. Is there any convention how to handwrite cardinal numbers, in particular, how to handwrite the continuum ($\mathfrak c$)
2
votes
0answers
46 views

When talking about periods of a function why is it common to introduce a factor of $2$?

In many books I have read, when talking about periodic functions, they tend to write the period as $2\omega$. Why do we need the $2$? I haven't come across any working where the factor of $2$ is ...
1
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0answers
48 views

asin, arcsin, $\sin^{-1}$ - is there any convention?

I've seen multiple forms how the arc sine is marked. But is there any convention which form is mostly being used? Does this depend on the country?
2
votes
1answer
42 views

Skeptical about (my understanding of) wikipedia's definition of a reflective subcategory.

I am self-learning category theory (though, at this point, I no longer remember what got me started), and I have encountered a troubling definition on wikipedia. The formal definitions of (full) ...
1
vote
1answer
26 views

What's the usual convention for directional derivatives in the $0$ direction?

Depending on the source, the definition of the directional derivative does not include the restriction that the direction vector be of unit length. In this case, it seems to me that we can then in ...
4
votes
0answers
57 views

Can a disconnected surface have a (negative) genus?

This question is rather about a convention. Is it possible (and conventional) to asign to, say the disconnected sum of two connected surfaces $X=\Sigma_h \sqcup \Sigma_g$ a genus? Since one has ...
2
votes
1answer
24 views

Vocabulary question: singularity for an analytic map

I have a question that is purely on vocabulary. My native language is not english, so I would like to know the usual convention for the following. When people say "let $f: X \to Y$ be an analytic ...
5
votes
1answer
2k views

The Degree of Zero Polynomial

I wonder why the degree of the zero polynomial is $-\infty$ ? I heard that, it is $-\infty$ to make the formula $\deg(fg)=\deg(f)+\deg(g)$ hold when one of these polynomials is zero. However, if that ...
10
votes
5answers
793 views

$\{1,1\}=\{1\}$, origin of this convention

Is there any book that explicitly contain the convention that a representation of the set that contain repeated element is the same as the one without repeated elements? Like $\{1,1,2,3\} = ...
6
votes
4answers
72 views

Is $\mp a$ actually different than $\pm a$?

So, the way I understand $\pm a$ as a general concept is basically as follows: $\pm a$ is really just two numbers, functions, or whatever $a$ represents, but the catch is that one of the $a$'s is ...
1
vote
1answer
109 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 ...
14
votes
5answers
2k views

use of $\sum $ for uncountable indexing set

I was wondering whether it makes sense to use the $\sum $ notation for uncountable indexing sets. For example it seems to me it would not make sense to say $$ \sum_{a \in A} a \quad \text{where A is ...
6
votes
3answers
119 views

Which is more simplified: $a\sqrt{b}$ or $\sqrt{c}$?

Which is considered more simplified (if it matters)? $a \sqrt{b}$ or $\sqrt{c}$ For example: $2 \sqrt{3}$ or $\sqrt{12}$
1
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0answers
32 views

“Second kind” orthogonal polynomials and functions

Recently I've been doing reading in the subject of orthogonal polynomials on the real line (OPRL). Such OPs arise in solving the three-term recurrence relation $$x ...
7
votes
1answer
165 views

What is $\varphi(0)$? [duplicate]

$\varphi$ is Euler's totient function. My question is: When/if $\varphi$ is defined at $0$, what is it usually defined as? Is there a "most natural" or more commonly accepted definition of ...
0
votes
1answer
39 views

Conventions adopted for extended reals

It is known that $0^0$ despite being an indeterminate limit form, is usually defined to be equal to $1$. I wonder whether similar conventions exist for some other "indeterminate forms" in the context ...
4
votes
2answers
65 views

Conjugacy in $S_n$ with composing permutations left to right vs. right to left

I realize there are two conventions for composing permutations. Left to right: $(1\ 2)(1\ 3) = (1\ 2\ 3)$ Right to left: $(1\ 2)(1\ 3) = (1\ 3\ 2)$ Among others, Dummit and Foote and Contemporary ...
0
votes
1answer
118 views

Assignment of initial probability values

Suppose a coin is tossed until a head is observed for the first time. It is given that the coin lands heads with probability $p$ and tails with probability $1-p$. Based on only this information, can ...
43
votes
11answers
8k views

What is the average of no numbers?

I have two programs that both behave nearly identically: they both take in any numbers you give them and can tell you the average and how many numbers were given. However, when you don't give them any ...
5
votes
2answers
126 views

Is $(a,a]=\{\emptyset\}$?

Let $a \in \mathbb{R}$, and consider the half open interval $(a,a]$. Is it correct to write this half open interval as $(a,a]=\{\emptyset \}$? Or $(a,a]=\{a \}$?
2
votes
0answers
48 views

Proper names for different representations of the same formula

I would like to know what to call formulas that are all on one line and what to call the same formulas that are on multiple lines. One line example: P ÷ TVD ÷ 0.052 Multiple line example: ...
1
vote
1answer
38 views

What topologies are placed on the domain and range of the characteristic function?

under consideration is: $\mathbb{1}_{[0,1)}:\mathbb{R}\to\{0,1\}$ $$\mathbb{1}_{[0,1)}(x)= \begin{cases} 1,& 0\leq x<1\\ 0,& \text{otherwise} \end{cases}$$ My first question is that I don't ...
0
votes
0answers
28 views

Vector in vector notation

I'm a bit confused as far as notationally differentiating between row and column vectors goes. Suppose I define a column vector $$\boldsymbol{a} = (a_{1}, a_{2})^{T}$$ and another column vector ...
1
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2answers
85 views

Why is the potential function defined differently in physics and calculus?

I am very familiar with the concept of a potential function, and potential energy, from calculus-based physics. For instance, if we have the familiar force field $\mathbf{F} = -mg \,\mathbf{j}$, then ...
-1
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3answers
57 views
0
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0answers
25 views

notation for contragredient matrix

Is there a standard notation for denoting the contragredient of an invertible matrix $A$. (The contragredient matrix of an invertible matrix is the inverse of its transpose).
3
votes
0answers
54 views

Conjugation of permutations

In the group $S_n$ I usually use the fact that if $(a_1 a_2 \dots a_r) \in S_n$ is an r-cycle and $\sigma \in S_n$ then $\sigma (a_1 a_2 \dots a_r)\sigma^{-1} = (\sigma(a_1)\sigma(a_2) \dots ...
3
votes
0answers
78 views

Writing a Series of Equalities and Inequalities across Several Lines

What is the convention for writing a series of successive equalities and inequalities across multiple lines? Let me explain. Let $E_k$ denote an expression; for example, $E_0$ could be a sum or an ...
1
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0answers
64 views

Matrix transponse in tensor notation

In this paper http://www.ita.uni-heidelberg.de/~dullemond/lectures/tensor/tensor.pdf at the end of chapeter 2 the author says that in index notation a matrix is written as $A^\mu_{\;\;\nu}$ and its ...
2
votes
2answers
86 views

When (and why) did the convention that exponents are evaluated from right to left arise?

Earlier, I saw this question on Quora: X^Y^Z Which one do I do first? and the current most-upvoted answer is this: The ^ operator is not associative, so that: (X^Y)^Z is not the same value as ...
1
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2answers
193 views

0 as an element of the natural numbers [duplicate]

For what reasons would or wouldn't one want 0 to be the start of the natural numbers as opposed to 1? Why would one want it to be 1, or why wouldn't one?
0
votes
1answer
125 views

How to translate math technical terms?

What is a good way to translate mathematical technical terms? This can sometimes be hard because some words have different meanings in some language. For example: "eigenwert" (= "eigenvalue" ...
2
votes
0answers
79 views

Does typesetting of mathematical content differ in right-to-left languages?

Languages such as Arabic or Hebrew are written right-to-left. Does the way mathematical content is written differ in those languages? Some simple examples of which I would be interested to know how ...
1
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0answers
91 views

Unit rules and style convention for division

I'm trying to figure out the preferred way to write unit expressions and division is causing me some confusion. I'm aware of the negative exponent notation, but here I'm looking for a solution using ...