Questions tagged [convention]

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

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Is there a standard name for the boundary of a cube?

A distinction is commonly made between a ball (solid) and a sphere (the boundary of a ball). This distinction is made in other dimensions as well (e.g. circle versus disc, in 2D). From what I've seen ...
realityChemist's user avatar
1 vote
0 answers
43 views

Is there a general consensus regarding which term is the multiplicand, and which is the multiplier in basic arithmetic multiplication?

Is there a general consensus regarding which term is the multiplicand, and which is the multiplier in basic arithmetic multiplication? In my notes I stated that in the expression $a \times b$ the left ...
Steven Thomas Hatton's user avatar
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1 answer
71 views

Meaning of $\sin^{-1}()$ and $\sin^{(-1)}()$ [duplicate]

Which of $\sin^{-1}()$ and $\sin^{(-1)}()$ refers to $\arcsin(\sin(x)) = x$ and $\csc(x) = \frac{1}{\sin(x)}$?
Adler's user avatar
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When drawing commutative diagrams, how to represent dense embedding?

I am taking some notes in functional analysis and I would like to represent a "dense embedding" in a commutative diagram. However, I have not found any convention for this. My current ...
Xiaoyu Liu's user avatar
1 vote
0 answers
24 views

Notation for $k$-partitions of $n$ containing at least one summand equal to $s$

I am looking for whether there is any notation for the $k$-partition number of $n$ where the partitions must include some summand $s$. An example of the kind of notation I am looking for is $P_k^s(n)$....
user110391's user avatar
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2 votes
2 answers
82 views

Intuitions regarding Einstein Summation Convention results

This is my first question on the site, so I apologise in advance if it isn't very good. I've recently learnt about the Einstein summation convention and I'm somewhat familiar with the basics of the ...
TheInquisitiveOne's user avatar
8 votes
2 answers
241 views

Dubious tensor-hom adjunction for chain complexes in Weibel. The differentials are wrong; can we make them right?

$\newcommand{\hom}{\mathsf{Hom}}\newcommand{\tot}{\mathsf{Tot}}$The exercise $2.7.3$ from Weibel's "an introduction to homological algebra" is known to be incorrectly stated. However, even ...
FShrike's user avatar
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Conventions on subscripts and superscripts: "Math mode" or "text mode" for (relatively long) words?

Is there any mathematical convention on the mode of writing (relatively long) words in subscripts or superscripts, i.e. either with a Latex math mode or with a text mode? For example: math mode: $A^{...
Ommo's user avatar
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1 answer
151 views

In what order should the terms of a polynomial in several variables be written?

Given a polynomial in one indeterminate, it is standard to write it in the form $a_0+a_1x+a_2x^2+\dots +a_nx^n$ (increasing order of degree) or $a_nx^n+a_{n-1}x^{n-1}+\dots+a_0$ (decreasing order of ...
Joe's user avatar
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Hatcher hopf algebra sign convention

I am reading 3.C in Hatcher's algebraic topology, where I was introduced to a sign convention for the product in $A\otimes A$ $$(a\otimes b)(c\otimes d)=(-1)^{|b||c|}(ac\otimes bd)$$ Does anybody ...
DevVorb's user avatar
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2 votes
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What is the property called wherein permuting the input tuple of a function results in the same permutation in the output tuple?

A function f takes an n-tuple as input and gives an n-tuple as output. If permuting the elements of the input n-tuple of this function always results in the same permutation of the elements of the ...
WingedKnight's user avatar
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0 answers
44 views

convention for non-commutative multiplication tables

Is there a standard convention for multiplication tables for non-commutative multiplication? Should the first multiplicand be the rows or columns? That is, if we have * a b a a b b a b then is $ab ...
TomKern's user avatar
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Suppose $F(x)=\int_c^x f(t)dt$ and $f$ is not defined at $x=c$. Is there an agreed upon convention as to what $F(c)$ should equal?

Suppose $F$ is a function of the form $F(x)=\int_c^x f(t)dt$ and $f$ is not defined at $x=c$. Is there an agreed upon convention as to what $F(c)$ should equal? Firstly, given that $f$ is not defined ...
S.C.'s user avatar
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-1 votes
1 answer
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Who coined the term Orthonormal? [closed]

Does anyone know who coined the term orthonormal to refer to a basis that is orthogonal and normal. In such a poorly named mathematical world (looking at you conditionally convergent series) I think ...
I love orthonormal's user avatar
0 votes
2 answers
120 views

What is meant by "increases exponentially with time"?

The following qeustion states "you may assume Phoebe's speed increases exponentially with time", but only provides 2 data points from which to derive the model. Is this question lacking ...
ort's user avatar
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8 votes
2 answers
262 views

What is the proper term for the "n" and "r" in the combination/permutation (nCr, nPr) functions?

Just like when we add, the parameters are called "addends", and how division has a "dividend", "divisor", "quotient", and "remainder", what is the ...
Joshua Huber's user avatar
1 vote
0 answers
35 views

Normalization conventions for explicit tensor representations of a $k$-form

There are all kinds of confusing combinatorial factors that crop up in the exterior algebra, especially if you're trying to work with explicit array representations rather than abstract objects. I've ...
tparker's user avatar
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1 answer
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Correct mathematical notation for negative of $2^n$

Given n is an positive integer, I came across $-2^n$ and I was wondering if this is equal to case (1): $2^n$ for even values of n, and $-(2^n)$ for odd values of n or case (2): $-2^n$, no matter what ...
Mojtaba Mohammadi's user avatar
1 vote
1 answer
65 views

For projection matrices, which vector of the outer product should be complex conjugated?

I have a conjugation wrong somewhere in my definitions, and I can't work out where it is. I want to define the standard matrix for a projection operator. If you can provide correct and standard ...
Mikkel Rev's user avatar
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3 votes
0 answers
73 views

What is the convention for "large" families of sets?

Premises: definition (class): A primitive object. Left undefined. definition (proper class and set): A class is proper iff it is not a member of another class. A class which is a member of another ...
R. Burton's user avatar
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0 votes
2 answers
150 views

Naming convention for unused variables

First of all, I am coming from a computer science background so bear with me if this is a silly question :) I am trying to proof something with tuples of type $(a, b, c) \in Z$ where $Z \subseteq A \...
Frederik Hoeft's user avatar
2 votes
1 answer
94 views

Change of variable $2\pi$ in the Fourier Transform

Introduction: Apparently the coefficient $\frac{1}{2\pi}$ in the Fourier transform formulas (the FT and the IFT) can be either: in front of the FT, and not in front of the IFT in front of the IFT, ...
niobium's user avatar
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0 votes
1 answer
41 views

Is there a conventional order to write commutative parts of an expression?

This stemmed from an office discussion. Often when writing expressions, it feels like there is a more natural way to write parts of an expression that are commutative. For instance, it seems as though ...
scs-erin's user avatar
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1 answer
68 views

If $Y\subset Z$, is a function from $X$ to $Y$ also a function from $X$ to $Z$? [duplicate]

If $Y\subset Z$, is a function from $X$ to $Y$ also a function from $X$ to $Z$? I think both possible answers are plausible: One the one hand, a function $f$ from $X$ to $Y$ is often called an ...
Filippo's user avatar
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2 votes
1 answer
67 views

A question on how a vector can given by a variable

This isn’t a repeat question as I know the reasons as to why the identification is made; this question is about an adjacent topic: implementation. In differential geometry, it’s common to identify ...
Lave Cave's user avatar
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1 vote
0 answers
139 views

Notation for constraining a function over multiple ranges

I have a function f(x) = y, as well as a set of pairs of constraints in the form of ranges of x and ranges of y. In practice, x and y are both vectors. I'm trying to express this more mathematically, ...
parrowdice's user avatar
5 votes
3 answers
376 views

What is the name of the symbol $=$ in English?

What is the name of the symbol $=$ in English? Wikipedia says people use "equals sign" than "equality". Is it right? Is it to avoid ambiguity between the equality formula $(x = y)$ ...
Paalon's user avatar
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2 votes
0 answers
134 views

Is the origin included in polar half-lines/radial lines?

In the complex plane, $\arg(z)=\alpha$ defines a half-line starting at the origin at an angle $\alpha$ from the positive real axis, however the origin itself is not included in the half-line as $\arg(...
Typo's user avatar
  • 402
1 vote
1 answer
180 views

Convention for second derivatives in Matrix Calculus

I am trying to understand the layout conventions used in Matrix calculus as described on Wikipedia. For this question I want to assume numerator layout and a "standard" vector to be in ...
bananananabatman's user avatar
1 vote
1 answer
42 views

Did I find the vector projection correctly?

I was a bit worried if I followed all the conventions correctly or not. Let the vector projection of a vector $\vec{a}$ on a non-zero vector $\vec{b}$ is $\vec{a_1}$. My attempt: $$\vec{a_1}=\frac{(\...
tryingtobeastoic's user avatar
0 votes
1 answer
91 views

Should I be worried about putting brackets around derivatives when I'm using chain rule?

$$\frac{d}{d(2\cot\theta)}(\tan^{-1}2\cot\theta)\cdot\frac{d}{d(\cot\theta)}(2\cot\theta)\cdot\frac{d}{d\theta}(\cot\theta)\cdot\frac{d}{dx}\theta\tag{1}$$ $$\left(\frac{d}{d(2\cot\theta)}(\tan^{-1}2\...
tryingtobeastoic's user avatar
1 vote
0 answers
34 views

Is my solution acceptable if I use a different sign convention?

Problem: A ball of mass 0.15 kg is moving with a velocity of 12 m/s and is hit by a bat so that the ball is turned back in the complete opposite direction with a velocity of 20 m/s. The force of the ...
tryingtobeastoic's user avatar
1 vote
3 answers
291 views

Is "$\frac10=\frac10$" true or false?

Please read the full question (and the linked answer) before responding. This started out as much longer question about extending complete theories by partial functions. That question was effectively ...
R. Burton's user avatar
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1 vote
2 answers
73 views

If the symbol '$f^{-1}$' shows up as an assumption, can I automatically assert that $f$ is a function?

In Chapter 12 of Spivak's Calculus, the definition of the inverse of function $f$ is provided as: For any function $f$, the inverse of $f$, denoted by $f^{-1}$, is the set of all pairs $(a,b)$ for ...
S.C.'s user avatar
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0 votes
0 answers
69 views

How to indicate the direction of a vector?

Here, A and B are the initial and final points of the vector $\vec{AB}$ respectively. We can say that the direction of the vector is from A to B. However, can we also say that the direction of $\vec{...
tryingtobeastoic's user avatar
2 votes
1 answer
118 views

Why do many people in math use the phrase "almost always" when referring to irrational numbers vs rational numbers? (from a language perspective)

I understand what they mean by "almost always." E.G.: Statement $A$ is true $\forall x∈ \mathbb{I}$. Statement $A$ is false $\forall x∈ \mathbb{Q}$. Therefore statement $A$ is almost always ...
Bastion Banner's user avatar
0 votes
0 answers
259 views

How to denote a line and a line segment?

I am certain that the name of the line segment is $AB$. However, what about the line? Do we just call it $CD$?
tryingtobeastoic's user avatar
2 votes
0 answers
831 views

How do I denote a triangle?

According to wikipedia, A triangle with vertices A, B, and C is denoted $\triangle ABC$. Can I call the above triangle $\triangle ACB$ or $\triangle BAC$ or so on?
tryingtobeastoic's user avatar
0 votes
1 answer
685 views

Difference between implies and "turnstile" symbols (→ and ⊢) [duplicate]

According to Wikipedia's list of logic symbols: A → B means A → B is false when A is true and B is false but true otherwise. ...
Elliott's user avatar
  • 129
3 votes
1 answer
118 views

Why do different Fourier transform conventions not make a difference in physical applications?

In physics, we are used to at least two Fourier transform conventions. These are $$\tilde{f}(k)=\frac{1}{2\pi}\int_{-\infty}^{\infty}f(x)e^{ikx}dx,\\ f(x)=\int_{-\infty}^{\infty}\tilde{f}(k)e^{-ikx}dk$...
Solidification's user avatar
2 votes
1 answer
32 views

Is there a standard name for the second defining property of ideals?

Let $(R, +, \cdot)$ be a ring and $I \trianglelefteq R$ be an ideal. One of the defining properties of ideals is that: $$\forall x \in I\ \forall r \in R \qquad r \cdot x, x \cdot r \in I$$ Is there a ...
Anakhand's user avatar
  • 2,522
2 votes
1 answer
85 views

Proper way to write "simultaneously approaching" the limit

Say there is some correspondence between $x$ and $y$. If we know that $\lim\limits_{x\rightarrow0}y=0$, we can safely say that "$y$ approaches zero if $x$ approaches zero" without causing ...
Long Horn's user avatar
  • 145
0 votes
3 answers
76 views

Where does the summation convention break?

In my work I have spotted something "weird". Consider the matrix \begin{align*} M_{ij} =1-\delta_{ij}. \end{align*} I want to find $ M^{2} $ in terms of its components. So \begin{align*} ...
Maths Wizzard's user avatar
2 votes
3 answers
209 views

Why don't we use xor (or nand)?

Why don't we use xor more often in ordinary mathematics? For example, every integer is even xor odd; for every real number $x\ne y$, we have $x<y$ xor $x>y$; a graph is bipartite xor it contains ...
Okoyos's user avatar
  • 296
4 votes
3 answers
211 views

Are integration and differentiation really mutually opposite?

Scenario 1: Suppose, I have a function $f(x)$. Now, let me add 5 to it: $$F(x):=f(x)+5$$ Now, let me subtract 5 from $F(x)$: $$F(x)-5$$ $$f(x)+5-5$$ $$f(x)$$ If I add 5 to $f(x)$, I get $F(x)$. Again, ...
tryingtobeastoic's user avatar
1 vote
0 answers
96 views

Does $(a,a]$ equal $a$?

In one of my exercises, I had a statement of the form $\forall x \in (c,b]: \varphi(x)$. However, it was possible that $c$ could take on the value of $b$...in which case, $(c,b]=(b,b]$. Is it safe to ...
S.C.'s user avatar
  • 4,932
1 vote
1 answer
123 views

Lang's Introduction to Algebraic Geometry conventions

As I mention in my question regarding Lang's definition of a generic point of the variety, the conventions he follows in his book Introduction to Algebraic Geometry seem weird to me. He considers a ...
Dog_69's user avatar
  • 1,867
2 votes
1 answer
157 views

Is my process of doing this math accurate?

Problem: Find the points of trisection of the line segment AB, where $A\equiv(4,0), B\equiv(0,3)$ Process 1: Let the P & Q be the points of trisection. Let $x_1$ & $y_1$ be the abscissa and ...
tryingtobeastoic's user avatar
0 votes
0 answers
24 views

Is there a conventional term for this parametrization?

Given a function $f:\mathbb{R}\mapsto \mathbb{R}$, and scalars $a,b,c,d \in \mathbb{R}$, is there a conventional term for giving it the following parameters? $$g(x;a,b,c,d) \triangleq af(bx+c)+d$$
Galen's user avatar
  • 1,816
2 votes
1 answer
33 views

Y Combinator proper parenthesization and question about the order/precedence of

In lambda calculus, the $Y$ combinator : $$Y = \lambda f.(\lambda x.f(xx))(\lambda x.f(xx))$$ I'm trying to interpret it using the only two lambda calculus notational conventions I'm aware of, namely: ...
joseville's user avatar
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