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

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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
31 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
20 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 ...
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2answers
53 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
40 views

For right triangle ABC, which angle is right (convention)? [closed]

For right triangle ABC, which angle is right (conventionally)?
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0answers
8 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
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0answers
33 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
46 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
50 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
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2answers
49 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
79 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
24 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
90 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
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0answers
64 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
27 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 ...
0
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1answer
24 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
53 views

Are these equivalent? $\cos^2(5x) = (\cos(5x))^2$

Are these equivalent? $$\cos^2(5x) = (\cos(5x))^2$$
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3answers
49 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
88 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 $\mathbf {i}$ ...
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0answers
46 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
30 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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0answers
57 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 ...
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2answers
28 views

Summation and Product notation: Convention for when final index number is smaller than the first?

What, for example, are the following? $\sum_{i=5}^4i$ $\prod_{i=5}^4i$ Is there a standard convention for what they should be? My guess is that $\sum_{i=5}^4i=0$ and $\prod_{i=5}^4i=1$. Is that ...
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1answer
126 views

Choosing the definition of $\frac{\partial^2}{\partial x\partial y}$

Today, I answered this question and discovered that the definition of $\dfrac{\partial^2}{\partial x\partial y}$ is a matter of convention. For example this .edu link and this other .edu link use the ...
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1answer
50 views

Is there a convention regarding the capitalization of adjectives derived from proper names?

Many mathematical properties are derived from the name of a mathematician associated with them: "Abelian," "Noetherian," "Artinian," "Frobenius (algebra, category, etc...)," "Cauchy," etc. It seems ...
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2answers
26 views

Is it correct to define variables and functions that are more than one character?

Most of the time (at least at my high school student level), we are using variables such as a, b or $\theta$, and functions such as f, g etc... But would it be possible to use multiple characters ? ...
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2answers
14 views

Rationale behind tuple notation for structured sets

Defining structured sets typically involves the convention of using a tuple of some sort; for example, the real line can be thought of as the quadruple $(\mathbf{R},+,\cdot,<)$. But this convention ...
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1answer
85 views

Is there any convention regarding the order of operation of the binary modulo operator?

Is there any predominant convention as to where the binary modulo operator (i.e., the variant of the modulo operator that is not applied to a whole equation) ranks in the order of operations, in ...
0
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4answers
146 views

Why is $0^0$ also known as indeterminate? [duplicate]

I've seen on Maths Is Fun that $0^0$ is also know as indeterminate. Seriously, when I wanted to see the value for $0^0$, it just told me it's indeterminate, but when I entered this into the exponent ...
6
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1answer
74 views

The convention for speakers to refer to themselves at the board with a single initial

This question is being asked on behalf of a graduate student in my department. When and where did the tradition start of a seminar or colloquium speaker using just the first initial of the speaker's ...
6
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9answers
142 views

Why is empty product defined to be $1$? [duplicate]

For example $\prod_{2 \le j < 1} 2^j= 1.$ How does that happen?
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1answer
100 views

Einstein summation convention differential

I'm just learning this convention, and at times I'm a little lost, like now. I have to calculate the following, knowing that $a_{ij}$ are constants such that $a_{ij}=a_{ji}$: $$ ...
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0answers
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How to write upper and lower generic limits of a definite integral

I have an integral whose upper and lower limits depends on the probabilty distribution chosen for the variable, $x$, I am integrating on. For example, if I consider that $x$ is normally distributed ...
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1answer
29 views

Nested square brackets in tensor indices

I know that using square brackets on tensor indicies denote the anti-symmetric part $$ T_{[ab]} = \frac{1}{2} \left( T_{ab} - T_{ba} \right)$$ I now have to prove that $$ T_{a [[bc]d]} = T_{a ...
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1answer
30 views

Question about sums with a negative limit for the index

To me, it looks like we have $\;\sum_{i = 1}^{0} x_i = 0\;$ and $\;\sum_{i = 1}^{1} x_i = x_1\;$. What happens if I write the following? $$\;\sum_{i = 1}^{-123} x_i\;$$ Would this be defined?
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The simply connected form of a semisimple algebraic group

Let $G$ be a semisimple algebraic group over an algebraically closed field $k$, so that $G$ is an almost-direct product of its minimal closed connected normal subgroups of positive dimension, ...
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1answer
93 views

Quantities $g_2$, $g_3$, $\Delta$

This question is somewhat related to this one. Let $\lambda$ be the modular lambda function. Greenhill (Elliptic Functions, p. 57) states that we may put $$g_2 = \frac{1 - \lambda + \lambda^2}{12}, ...
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0answers
56 views

How to show proper set inclusion/exclusion? Please don't give me the solution.

I found this problem from an online source. I've just got two question 1) I think there is a typo in the solution, it should be $(x_n) \in \ell_1$ right? 2) I am guessing $c_0 \subsetneq ...
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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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2answers
51 views

Combinaision of two functions

Let us denote $X_0 = \{x, y\}$ and $X_1 = \{a, b\}$ two disjoint sets of variables; let us denote $V$ a set of values. I have two functions $f_0 : X_0 \rightarrow V$ and $f_1 : X_1 \rightarrow V$, ...
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In which field of science that we can prove $0! =1$ and what i can say to studentof high school if he asked about it's prove ?? [duplicate]

In mathematics there are some data , we have took them by convention and mathematics is not able to show us them proves , now want just to know if the "convention" term enough mathematics ...
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11 views

Symbol or name for Basismatrix of Linear Programming

This question is about the Basismatrix in the context of Linear Programming. Basically (haha!) we have the Matrix of the standard (or normal) form, which consists of (A|E) with the coefficient matrix ...
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2answers
64 views

Beginner questions about Sets.

I have a quick question in regard to sets. I am a little confused when I see the notation $A\subseteq B$. How is this different than the sets $A$ and $B$ being identical? I guess some of the confusion ...
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2answers
533 views

Euler-Angle convention

I'm studying the course on edx and can't answer this question: How many different Euler angle conventions are there?
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37 views

problems on define set with polynomials

I'm trying to say set A is the set of nonnegative integers that not of this two forms $3x^2 + (6y-4)x - y\ $ and $\ 3x^2 + (6y-2)x + (y - 1)$, for example: $4=3 \cdot1^2+(6 \cdot1-4) \cdot 1-1\ $ is ...
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1answer
121 views

Which is the best notation for a sequence?

In a set, the order of its elements is (as far as I know) not important; in a sequence, the order of its elements is important. Which is the notation I should use in order to define a sequence? I ...
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1answer
68 views

Is there a convention for power of a half being the positive square root?

I know the $\surd$ sign refers to the positive square root. Does the exponent 1/2 mean the positive square root too by convention? I ask because I'm converting from parametric to cartesian here... ...
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1answer
62 views

Does an integral without an integrand imply the integrand is $1$?

This is a question concerning mathematical convention. If we see something like $$ \int_a^b dx $$ Does this imply that $$ \int_a^b dx = \int_a^b 1\ dx\text{?} $$
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1answer
124 views

Prove thoroughly: If the degree of all vertices is greater or equal to $\frac{|V| - 1}{2}$, then the simple graph is connected.

I am struggling to write a good, thorough proof. The proof is supposed to be logically rigorous, correct and complete (e.g. no hidden assumption). Moreover, style is important - the proof should be ...
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2answers
73 views

Should “together with” be taken as slang for an n-tuple?

When an algebraic structure is defined, it is often defined as a set $S$ "along with"/"together with"/"having" operations $\circ_1, \circ_2, \ldots, \circ_n$, and "denoted" by $(S, \circ_1, \circ_2, ...