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

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4
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1answer
57 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}, ...
0
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0answers
18 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 ...
37
votes
11answers
7k 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 ...
29
votes
10answers
3k views

What could be better than base 10?

Most people use base 10; it's obviously the common notation in the modern world. However, if we could change what became the common notation, would there be a better choice? I'm aware that it very ...
0
votes
2answers
43 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 $f_1 : X_1 \rightarrow V$, ...
8
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3answers
2k views

What does a “convention” mean in mathematics?

We all know that $0!=1$, the degree of the zero polynomial equals $-\infty$, the interval$[a,a)=(a,a]=(a,a)=\emptyset$ ... and so on, are conventions in mathematics. So is a convention something that ...
0
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2answers
253 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?
3
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2answers
63 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, ...
3
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0answers
93 views

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 ...
1
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0answers
9 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 ...
0
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2answers
41 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 ...
0
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1answer
38 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 $$ \int_a^b dx = \int_a^b 1\ dx\text{?} $$
1
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0answers
36 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 ...
1
vote
2answers
163 views

Combine a rotation matrix with transformation matrix in 3D (column-major style)

I'm trying to concatenate a rotation matrix with a 4x4 homogeneous transformation matrix with column-major convention. I want this rotation matrix to perform a rotation about the X axis (or YZ plane) ...
2
votes
1answer
100 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 ...
0
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0answers
36 views

Are there official names for these functions?

$\newcommand{\sgn}{\operatorname{sgn}}$ Does anyone know if the simple function $$ y(x)=x^2\sgn(x)$$ or alternately $$ y(x)=x|x|$$ has any (official) name in mathematics or engineering? or ...
11
votes
5answers
544 views

What are reasons why some symbols in mathematical logic are not standardized?

Why is so hard to find a standardisation regarding symbolism and/or terminology in Mathematical Logic ? We see again and again students asking if e.g. $\rightarrow$ and $\implies$ means the same ...
1
vote
1answer
45 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... ...
2
votes
2answers
88 views

Game Theory: players' gender convention?

What is the Game Theory convention of using gender terms (male/female) for the players? I found only one reference suggesting that odd-numbered players are male and even-numbered players are female. ...
1
vote
1answer
61 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 ...
3
votes
2answers
138 views

Usage of $\cdot$ in calculus

I often find myself caught in the dilemma of whether or not to use the symbol $\cdot$ in calculus. Take for example, the chain rule: $$\frac{dy}{dx} = \frac{dy}{du}\cdot\frac{du}{dx}$$ Is the ...
15
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3answers
664 views

Starting sentences with mathematical symbols.

I apologise if this is a duplicate in any way or is too opinion-based. To what extent is it best not to start a sentence with a mathematical symbol? I find that when trying to solve a problem or ...
9
votes
3answers
262 views

Rationale for a convention: Why use the semiperimeter in Heron's formula?

Heron's formula says that the area of a triangle whose sides have lengths $a, b, c$ is $\sqrt{s(s-a)(s-b)(s-c)}$ where $s=(a+b+c)/2$ is the semiperimeter. It can also be stated by saying that the ...
1
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0answers
35 views

Graph diameter of a single vertex?

Convention-wise, given the simple graph with a single vertex, what is the graph diameter? I can see three options, zero, since there is a trivial path from the vertex to itself. infinity, since ...
0
votes
1answer
86 views

Is there a symbol/ way to mathematically indicate an answer?

I know this is going to sound rather contrived, but I was wondering if there was a symbol to indicate a solution to a problem. I'm a student studying engineering and constantly shift between notations ...
0
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0answers
38 views

Given a set of rotation matrices, is it possible to determine the rotation conventions employed?

Given three rotation matrices, is it possible to determine the conventions used in defining them? These conventions include: passive or active transformation, pre- or post-multiplication, right- or ...
3
votes
1answer
57 views

Commas between adjectives [duplicate]

Is it correct to use these expressions without commas (as written below)? A finite simple group. A finitely generated abelian group. A finitely generated torsion-free abelian group. A ...
0
votes
1answer
49 views

Name and notation convention for “unnormalized probability”

Given a finite set of non-negative numbers $S={s_1,...,s_n}$, we can divide them by a normalization constant $Z$ (i.e. their sum) to get a probability distribution. Then we typically say (and write) ...
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0answers
40 views

shouldn't we specify the topology when we talk about Borel $\sigma$-algebras?

Maybe this is me being pedantic, but this thought has just occurred to me. The Borel $\sigma$-algebra on X is the smallest $\sigma$-algebra containing all open sets. When we talk about Borel ...
0
votes
2answers
79 views

Question about secant and cosecant.

Ok so if we take a right triangle and consider an angle $\alpha$ we get the following: From here we can define the fundamental trigonometric functions sine and cosine where ...
2
votes
1answer
47 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 ...
2
votes
2answers
94 views

why function argument is on right side $f(x)$ rather than on left side as $xf$

Is there an advantage for writing function arguments on the right side as $f(x)$ rather than on the left side as $xf$? The latter looks more natural if we think about it in diagram as $domain ...
1
vote
1answer
48 views

Notation in functions spaces

I'm wondering if there is a convention for the following. Let $g:\mathbb{R}^2\to \mathbb{R}$ be given and u in $C^1(\mathbb{R})$. I'm looking for a notation for $g(x,u(x))$ is in the space of ...
8
votes
1answer
112 views

Wikipedia claims that number theorists tend to prefer $0 \notin \mathbb{N}$. Is this actually true?

According to wikipedia here: $\mathbb{N}$ means either $\{ 0, 1, 2, 3, ...\}$ or $\{ 1, 2, 3, ...\}.$ The choice depends on the area of mathematics being studied; e.g. number theorists ...
0
votes
0answers
67 views

Convention on the order of scalar multiplication (Multiplier vs multiplicand)

Is there a convention on the order of scalar multiplication? I know there were questions before mine, but I would like to know if such distinction is culturally dependent. This came from a news in ...
2
votes
1answer
111 views

Category of topological pairs

Is there a standard abbreviation for the category of topological pairs? I have searched for it in vain.
0
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2answers
175 views

Fourier transform convention: $\frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty} f(x)e^{\pm ikx}dx $?

I've come across the Fourier transform being defined as: $$\tilde{f}(k)=\frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty} f(x)e^{ikx}dx$$ But this convention is not present in the Wikipedia article. The ...
0
votes
1answer
116 views

Normalization of Orthogonal Polynomials?

The generalized Rodrigues formula (Hassani, Mathematical Physics, p. 174) is of the form $$p_n=K_n\frac{1}{w}\left(\frac{d}{dx}\right)^n(wp^n)$$ The constant $K_n$ is seemingly chosen completely ...
9
votes
4answers
215 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 ...
2
votes
1answer
86 views

Why is $m$ used as the variable for slope in slope-intercept form?

I was wondering if you could answer a question I have on slope intercept form of a linear equation. I know its $y=mx+b$, but why is it $mx+b$? Don't get me wrong. I know that $m$ is the slope and $b$ ...
2
votes
2answers
116 views

What is a vector with a single non-zero component called?

What do you call a vector with a single component, e.g. $[a, 0, ..., 0]$ or $[0, b, 0, ..., 0]$, where $a, b$ are any non-zero number? I'd like the language to differentiate from a vector with ...
18
votes
6answers
521 views

Is there a fundamental reason that $\int_b^a = -\int_a^b$

Is there a fundamental reason that switching the order of the limits in an integral results in the negative, i.e., $$\int_b^af(x)\,dx = -\int_a^bf(x)\,dx?$$ As far as I can tell, this is just chosen ...
0
votes
1answer
33 views

Value expressions

What is the value of the expression: $\sum_{k=0}^{d}b^{k}\left[\begin{array}{c} d\\ k \end{array}\right]\prod_{i=0}^{k-1}\left(c-b^{i}\right) $ for $ k = 0 $? In particular, what is then the value ...
3
votes
3answers
174 views

$x^{y^z}$: is it $x^{(y^z)}$ or $(x^y)^z$?

Of the following, why is a usually considered true, and for what reason other than "tradition" and "more convenient"? a: ${x}^{y^z} = x^{(y^z)} \neq {(x^y)}^z$ b: ${x}^{y^z} = {(x^y)}^z \neq ...
0
votes
1answer
59 views

Order of operations: Matrix product and hadamard product

Is there any convention of the order of operations in a term with both ordinary matrix multiplication and hadamard (elementwise) multiplication? Obviously, $$ A ( b \circ c ) \ne (A b) \circ c $$ ...
14
votes
6answers
3k views

No radical in the denominator — why?

Why do all school algebra texts define simplest form for expressions with radicals to not allow a radical in the denominator. For the classic example, $1/\sqrt{3}$ needs to be "simplified" to ...
5
votes
1answer
277 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 ...
4
votes
2answers
83 views

A question on notation: $u(x,y)$ vs. $u(x+iy)$.

In Tao's complex analysis notes, he uses the convention that $$f(z)=u(z)+iv(z)= u(x+iy)+iv(x+iy)$$ implying that the functions are $$u,v:\mathbb{C} \to \mathbb{R}.$$ But in other places I see the ...
5
votes
5answers
254 views

No difference between $0/0$ and $0^0$?

I have seen discussions about both $0/0$ and $0^0$ and they differ a bit in the way that most seem ok with calling $0/0$ "undefined", while the $0^0$ discussion still seems like a dispute. If this is ...
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vote
4answers
122 views

Are there two conventional definitions of “holomorphic”?

In Walter Rudin's Real and Complex Analysis, second edition, on page 213, two definitions are stated. One of them says the derivative of $f$ at $z_0$ is $$f'(z_0)=\lim_{z\to ...