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

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Is there no (basic) math webfont? [on hold]

This is a typographical question that is too esoteric from the viewpoint of graphicdesign.stackexchange --- but a rather natural occurrence for daily users of math, so I think this is the place to put ...
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2answers
44 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 ...
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60 views

Is there an open / established ontology 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 ...
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1answer
57 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 ...
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2answers
592 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 ...
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5answers
474 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 ...
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0answers
63 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 ($\mathfrak c$)
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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 ...
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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?
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1answer
38 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) ...
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1answer
21 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 ...
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48 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 ...
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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 ...
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1answer
1k 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 ...
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5answers
752 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\} = ...
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4answers
70 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 ...
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1answer
107 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 ...
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5answers
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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 ...
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3answers
116 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 $\sqrt{12}$
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0answers
30 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 ...
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1answer
158 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 ...
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1answer
37 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 ...
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2answers
60 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 ...
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1answer
116 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 ...
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11answers
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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 ...
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1answer
49 views

Does using the notation $f(x)$ imply the relation is a function? [closed]

If I have a mapping that is not a function, can I still use $f(x)$ to describe it?
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2answers
124 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 $(a,a]=\{a \}$?
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0answers
47 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: ...
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1answer
34 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 ...
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0answers
23 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 ...
0
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2answers
71 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 ...
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3answers
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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).
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52 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 ...
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0answers
66 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 ...
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0answers
60 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 ...
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2answers
72 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 ...
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2answers
174 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?
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0answers
35 views

What is the appropriate way to indicate that a long statement is continued on the next line?

When handwriting a long mathematical statement or equation, what is the clearest way to indicate that it is continued on the next line uninterrupted? I've considered defining a variable to equal ...
0
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1answer
114 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" ...
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0answers
76 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 ...
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0answers
75 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 ...
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1answer
40 views

Has the functions having countably infinite image, but finite when the domain is bounded, a conventional name?

I'm trying to find properties for functions that cover the following properties and wondering if they have a formal name to search more efficiently. The function $f(x)$ cover the following ...
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1answer
56 views
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55 views

Special Case of Summation

Hello what would be the solution to the summation over the range from 1 to 0? $$ \sum_{1}^{0} = ? $$ My guess is -1 or 0, but I can't find any reference to this case.
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4answers
93 views

Why do texts frequently define $\mathbf {i}$?

Often when I see a formula containing $\mathbf {i}$, it will be accompanied by the definition $\mathbf {i^2 = -1}$. Why don't we just assume that most students of advanced math know what $\mathbf {i}$ ...
2
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0answers
65 views

Einstein summation convention

I am not sure how to expand the following expression with regard to the Einstein summation convention. More specifically, I have: \begin{equation} a_{ij} = b_{i, j} + b_{j, i} + c_{ij, kk} \\ c_{ij} = ...
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1answer
57 views

Convention for chain of inequalities

Sorry if this is not the right place to ask. In the proof of a theorem, I basically want to write $A<B$, and $B=C$, thus $A<C$ as a chain of inequalities. I am not sure if there is a convention ...
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3answers
562 views

Notation: permutation and its inverse

Consider the sequence $S = (A, B, C, D, E)$ and the permutation $\pi = (4, 1, 3, 5, 2)$: Which of the following is true? $$ \pi(S) = (B, E, C, A, D) \quad and \quad \pi^{-1}(S) = (D, A, C, E, B) ...
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84 views

Is is possible to define a sign convention for eigenvectors calculated with a small uncertainty?

I'm working with a numerical method that involves the diagonalization of a real, symmetric $n \times n$ matrix $H$. Now obviously the sign of the (normalized) eigenvectors $\phi_i$ is not well ...