Questions tagged [convention]

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

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2
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1answer
29 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 ...
1
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1answer
50 views

Proper way to write "simultaneous 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 ...
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0answers
17 views

Representing multidimensional matrix on a plane [closed]

I'd like to know if, given a multidimensional matrix, it is possible to draw it on a plane. Maybe there is a convention to do that.
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3answers
57 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*} ...
2
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2answers
114 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 ...
4
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3answers
83 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, ...
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0answers
90 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 ...
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1answer
62 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 ...
2
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1answer
89 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 ...
2
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1answer
21 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: ...
2
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1answer
92 views

According to which authoritative source, where in a conventionally ordered list of constants does $\pi$ go? (Eg, "$h\pi$" vs "$\pi h$") [closed]

Where in a conventionally ordered list of constants does $\pi$ go? For example, if you look at the attached image, you can see that in my last answer, I’ve put $h \pi$. But in the answer section of ...
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0answers
14 views

Considerations when creating piecewise functions

I am asking about the dos and don'ts of piecewise expressions. First of all, there's the question of completeness versus clarity. Being as complete as possible can lead to long piecewise expressions ...
1
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1answer
37 views

Is there a specific notation to denote which angle is the orthogonal angle of a right triangle?

If an exercise says "the right triangle $ABC$" is there an order of the letters to signify which angle is the orthogonal angle? For example $ABC$ is a right triangle means $\hat B=90$ ...
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0answers
10 views

Notation for set of maximal sequences

Is there some established notation for "maximal sequence"? I'm trying to write the following: Let $[a,b]$ be the sequence of integers from $a$ to $b$ (many other ways to write it given here)....
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0answers
33 views

What variable should i use to represent a small value?

I am writing a computer code. I need to name a variable that represents a small offset. Typically, I'd use epsilon or delta for ...
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2answers
66 views

$\bmod\!$ operator precedence: does $\,a\bmod b+c\,$ mean $\,(a\bmod b)+c\ $ or $\ a\bmod (b+c)\,$?

$\bmod\!$ operator precedence: does $\,a\bmod b+c\,$ mean $\,(a\bmod b)+c\ $ or $\ a\bmod (b+c)\,$? My intution is that a mod b + c == (a mod b)+c, but, in Wolfram ...
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1answer
93 views

Do uppercase letters mean anything special in Mathematical Reasoning problems?

I have been asked to determine whether the following is a tautology or not: $((p \wedge q) \wedge \sim P)) \rightarrow P $ I am confused whether the uppercase 'P' is just a misprint or it actually ...
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0answers
109 views

Where does the $2$ in Ricci flow come from?

I started learning about Ricci flow recently, which is always given as $$ \frac{\partial g}{\partial t}=-2\textrm{Ric}. $$ It would seem more natural to me to define Ricci flow instead by the equation ...
4
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2answers
73 views

Why is it natural to define reflections in terms of its hyperplane?

There are two ways to reflect a vector $v$ by another vector $u$. The first is to 'directly' reflect $v$ through $u$: where $v'=2P_uv-v$ with $P_u=\frac{uu^T}{|u|^2}$. The second way is to reflect $v$...
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2answers
232 views

Wedge sum of an empty set of spaces

In algebraic topology wedge sum is defined for a family of indexed, say by a set $\mathcal{I}$, spaces $X_i$ with points $p_i \in X_i$ as: $$ \bigvee_{i \in \mathcal{I}} X_i = \frac{\bigsqcup_{i \in ...
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1answer
57 views

Should upright math symbols stay upright when the context is italicized?

Consider the smallest infinite ordinal ω. Notice that it's typeset upright by default to denote that the meaning of the symbol is fixed. In normal text this causes no problems: Now we present the ...
2
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1answer
79 views

Is there a convention for divisibilty $a\mid \infty$?

The following problem: Let $G,H$ be groups and $\varphi: G\to H$ be a group homomorphism. Prove that $\mathrm{ord}(\varphi(g))\mid\operatorname{ord}(g)$. This is easy when $\operatorname{ord}(g)=n<\...
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2answers
185 views

Ambiguity in the property that opposite angles of a cyclic quadrilaterals are supplementary

Consider a convex cyclic quadrilateral ABCD. A basic property of one such quadrilateral is that $\measuredangle \, BCD + \measuredangle \, DAB = 180^{\circ}$. One way to settle this equality is by ...
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1answer
23 views

Is there standard terminology to describe these two different kinds of domain a relation can have?

When talking about relations, injections, surjection, etc… we usually consider two different sets of input to the relation. For example, the input sets might be $\{1, 2\}$ and $\mathbb{N}$. These two ...
5
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2answers
28 views

Terminology and notation for a zero-padded restriction of a function

I am a lowly data analyst, but I like to use standard mathematical terms and notation when possible. Here is the setting: given some function $f : \mathbb{R}^2 \rightarrow \mathbb{R}$, and some subset ...
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35 views

Naming complementary angle

Is there a simple, standard way of writing the complementary angle of $\alpha$, namely $90^\circ - \alpha$? And what about the supplementary angle?
1
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1answer
27 views

Conventional notation for congruence to multiple numbers

Is there a more concise notation for the following sentence? "Thus $ f(n) \equiv 0 \pmod{12} $ for all $ n \equiv x \pmod{12} $ where $ x \in \{ 0, 1, 3, 6, 7, 11\} $." Is this an acceptable ...
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0answers
61 views

How do you write the name of a cube?

This is kind of a silly question but here goes. Is there any accepted convention for the order in which you list the vertices when you write the name of, say a cube? (This could also be extended to a ...
0
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1answer
136 views

Can a proposition be false and its negation be false in Intuitionistic logic?

The principle of non-contradiction say that p and $\neg$ p can not be both true. If you consider the law of excluded middle as relevant, then either p or $\neg$ p is true, and thus the other is false ...
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0answers
53 views

Do mathematicians implicitly assume all random variable map to the real line?

I just want to confirm a convention in probability that whenever we talk about a random variable, we assume that the codomain is $\mathbb{R}$. That is, whenever $A$ is a random variable, $\text{...
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0answers
20 views

Name for the convention where a semicolon is use to separate variables from parameters

It is somewhat common to write $f(x_0,x_1;\ z_0,z_1)$ to indicate that $f$ is a function of $x_0,\ x_1,\ z_0,\&\ z_0$, but that the $z$ arguments should be thought of as fixed by the context, ...
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0answers
26 views

Summation and product convention

Is there a standard convention for iterated addition or product when the upper index is smaller than the lower index? That is, how to expand these terms: $$ \sum_{i=a}^b x_i, \\ \prod_{i=a}^b x_i $$ ...
3
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1answer
57 views

Is there a short symbology to express that $f$ is a morphism in $C$?

For the simple purpose of taking notes without writing too much, I'm wandering two things. Given the category $C$ is it ok to write $c \in C$ to express the idea that the object $c$ is in the ...
2
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2answers
53 views

If $f:A \to B$ is a real function, and $y\in B, $ Is Rudin's definition of $f^{-1}(y)$ commonly accepted as convention or not?

Let $f:A \to B\ $ be a function. In Rudin's PMA, at the bottom of page 24 and top of page 25, he states: If $y \in B, f^{-1}(y)\ $ is the set of all $x \in A\ $ such that $f(x) = y.\ $ This notation ...
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1answer
45 views

Notation for multilinear maps - is there a good reason why it is not common to write $\text{ML}(V_1\times\ldots\times V_n,W)$?

Since we write $\text{L}(V,W)$ for the set of linear maps from $V$ to $W$, it seems to suggest itself to denote multilinear maps from $V_1\times\ldots\times V_k$ to $W$ by $\text{ML}(V_1\times\ldots\...
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1answer
47 views

Where, if ever, is it proper (expected) to use a space? Where by convention is it [preferred, or preferred not] but allowed, or forbidden? [closed]

The only place I see a space (aside from within tables) inserted with some regularity is surrounding an equals sign to more clearly separate a right-hand from left-hand side of an equation. Aside from ...
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0answers
19 views

Can you write the differential operator at the back of an expression?

I'm a tutor for a course on optimization at my uni and today (while correcting exercise sheets) a student presented me with something like this: $$ 0 = (ax^* + b) \frac{\partial}{\partial x} $$ Where ...
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0answers
57 views

"Big ear" of polygons: proper nomenclature

I've developed a polygon triangulation algorithm which uses a process similar to the "Graham Scan" to remove convex "portions" of a concave polygon. I couldn't find the proper ...
7
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1answer
324 views

Is there any official, specific convention that defines whether an expression is considered "Simplified"?

I see all the time in high school math textbooks problems saying to "simplify" an expression. Their explanations of what it means for an expression to be "simplified" is a bit ...
0
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1answer
21 views

Convention for notation and set representation, for set of all $m\times n$ $F$-valued matrices.

Is it conventional/understandable to denote the set of all $m\times n$ matrices over $F$ as $\left(F^n\right)^m$, as $m$-tuples of column vectors, just like $n$-tuples are used as $n$ dimensional ...
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1answer
27 views

How to denote a range of elements in a row array?

Let's say I have a row vector $\vec{x}_i \in \mathbb{R}^{1\times T}$. You can consider it as the $i$-th time-series from a set of time-series. I want to index a subsequence from $\vec{x}_i$ from $t1$ ...
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1answer
78 views

Difference between convention for matrix multiplication of vector in algebra and computer science

In algebra, we typically write $Ax=b$ when we wish to multiply a $n$ dimensional $x$ vector by matrix $A$, requiring $A$ of course to have $n$ columns. Yet, in computer science, I typically see $xA=b$,...
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1answer
68 views

What is the difference between $\partial_\mu$ and $\partial^\mu$?

I am taking quantum field theory this semester. There we use the Einstein Informalism. But I have never seen it before. I understood that if there are two letters on one letter, that this is a matrix, ...
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1answer
51 views

Half-values at discontinuities in Riemann's prime counting function

Wikipedia (here) and MathWorld (here) disagree about the behaviour of Riemann's prime counting function $\Pi(x)$ at points of discontinuity. The function is defined by $$\Pi(x)=\sum _{p \text{ prime} \...
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1answer
72 views

How often are vulgar fractions used in mathematical writing?

In (American) primary school, they first teach you how to reckon with simple fractions in numerator-over-denominator "vulgar" form, often using the image of a pie as an illustration. They ...
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0answers
29 views

What is the convention for referencing matrix indices with values greater than 9?

I would like to reference elements of a matrix $A$ such that each element can be found by its corresponding row and column position. Namely, $a_{ij}$ where $i$'s are rows and $j$'s are columns. The ...
6
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3answers
612 views

Ring theory conventions - Zero ring, local homomorphisms

Just wondering about conventions dealing with the zero ring and the zero scheme. Does the category of schemes have an inital object? Is the zero ring considered local? For the purposes of scheme ...
3
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0answers
62 views

Why $T_pM$ instead of $TM_p$?

If $E\to M$ is a fiber bundle, it's convention to write 1. $E_p$ for the fiber at $p$, 2. $E^*$ for its dual bundle. Exceptionally, for the tangent bundle $TM\to M$ almost every author writes 1. $T_pM$...
3
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2answers
199 views

What are the domain and values of binomial coefficients $ n \choose k $ for any integer $n$ and $k$, and why?

This is a question about "nasty details" of the binomial coefficients. I would like to understand the definition of binomial coefficients $ n \choose k $ for general integers $n$ and $k$. ...
1
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1answer
235 views

Dot product with Einstein summation convention (index notation)

My professor, when proving: $$a \cdot b = a_ib_i$$ wrote: $$(a_i \hat{e}_i)\cdot(b_j \hat{e}_j) = (a_ib_j)(\hat{e}_i\hat{e}_j)$$ My doubt is: Are we allowed to treat the dot product as ordinary ...

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