Questions tagged [convention]

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

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6
votes
3answers
459 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 ...
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0answers
17 views

Is there a best practice for naming mathematical objects? [closed]

Does anyone know of a guide for selecting (single letter) names for variables and functions etc. in an applied mathematics text when there is no established standard?
2
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0answers
48 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
43 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
36 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 ...
2
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1answer
92 views

Why use random variables instead of probability spaces

When talking about various ways to model something probabilistically, many authors prefer to use random variables, instead of probability distributions. Of course, this difference is more of a point ...
0
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1answer
65 views

In standard set theory is a statement containing both a union and intersection but no parentheses disallowed?

Most discussions of set theory with which I am familiar assign equal operator precedence to $\cap$ and $\cup$. This may sound like a ridiculous question, but I never thought about, nor do I recall ...
2
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1answer
124 views

confusion regarding treatment of $dx$ in a physics problem

Consider a fixed, positive Point charge $q1$, kept at the origin. Another (positive) charge, $q2$, is being brought from $\infty$ to the point $(r,0)$, by an external agent slowly. We wish to ...
5
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1answer
60 views

Can an axiom in FOL have recursion?

Lately, I've been interested in playing around with seeing how powerful a set theory can be with a single axiom. A while, ago I made this naive axiom schema; dubbed the axiom schema of propagation (...
-1
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1answer
64 views

Why doesn't $\sum_{n=0}^\infty2^n=-1$?

Now of course I'm not stranger to the fact that adding finite (and in many cases - infinite) amount of positive numbers always yeilds a positive number, but in many cases, often the finite limit isn't ...
0
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4answers
95 views

Conventional to write the derivative of $|x|$ wrt $x$ as $\frac{x}{|x|}$?

This might be a naive question, but it sometimes confuses me. It's known that the derivative of $|x|=\frac{x}{|x|}$. Is it conventional that the absolute value appears in the denominator and not $\...
5
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0answers
76 views

Formatting in Latex [closed]

Is there any consensus about when to use inline math mode and when it is more appropriate to use display math mode when writing in latex (in formal math writing)? When writing, I feel that it is often ...
0
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1answer
42 views

What's another name for the integral function?

I know this is certainty a basic question, but I'm wondering what you could use as an alternate name for the integral of a function. That is to say; $$\text{In } \int f(x)dx=F(x) \text{, } f(x) \text{ ...
0
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1answer
49 views

Group theory convention

When I was an undergraduate, in my first courses in group theory the convention was that we always act on the right, so if $f:G\rightarrow H$ is a group homomorphism, then we would write $(g)f$ for ...
1
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1answer
35 views

How would one notate the subset of the rationals with terminating decimal expansions?

Is there a convention for notating a subset of the rationals with restrictions on the denominators? I'd prefer there to be a relatively intuitive and concise notation for the set $\{\frac{n}{10^m}:n,m\...
2
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0answers
89 views

Pronouncing the symbol $!$ as understood as a morphism in category theory.

How does one pronounce the symbol $!$ as a morphism in category theory? I heard it spoken as, "shriek" here, but I don't know whether that's the convention or not. In my opinion, "exclamation mark" ...
1
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1answer
57 views

Why does $\bigcup_{i\in\emptyset}i=\emptyset$ (the empty union)

It seems that the consensus/convention is that the empty union, $\bigcup_{i\in\emptyset}i=\emptyset$ At first glance this seems intuitive, however please consider my following arguments and let me ...
2
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2answers
40 views

How I convince my self that if we say $\epsilon >0$ we must refer to small quantity?

Many mathematical definitions almost used $\epsilon >0$ to define any mathematical notion, for example if we want to give definition to the convergence of sequence we say " $\forall \epsilon >0 ,...
1
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1answer
28 views

Is there a convention when notating sets or summations?

I have a background in physics and usually when you denote a set, summation or for-loop one says "for every i in N". The index is usually i and the total number of the set or population is N. Then you ...
0
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1answer
21 views

Plot Orientation of the 2d/3d Cartesian coordinates

Per convention, we draw a 2d Cartesian coordinates system as a '+' with the x-axis pointing right and the y-axis pointing up. When it comes down to making the plot 3d, by adding a z-axis, it's pretty ...
0
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1answer
66 views

Is $y=0^x$ really a function?

I know that there are three main options when it comes to dealing with $0^0$: $$0^0=0$$ $$0^0=1$$ $$\nexists x(x=0^0)$$My question is, do we have to assert that one of these conditions is true in ...
1
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2answers
70 views

Why is it standard convention to denote dual vectors as row vectors when using coordinates?

I found this claim in my lecture notes on real analysis in the chapter on the gradient. When using coordinates, the standard convention is to denote vectors as columns, and covectors as rows. ...
1
vote
1answer
18 views

How many numbers between x and y means inclusive or exclusive generally?

If someone says: How many numbers are a multiple of $10$ between $1$ and $100$? and does not mention whether this is $[1, 100]$ or $(1, 100)$, what is the general consensus in the math world on ...
3
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0answers
49 views

Use of the Adjective “Invariant” in Mathematical Literature

I'm currently reading Lee's Introduction to Smooth Manifolds, in which he makes a remark along the following lines: "The next corollary can be viewed as a more invariant version of the rank ...
3
votes
4answers
181 views

Doubt about Empty Set's definition as a Set.

A set is a well-defined - collection of distinct objects. The objects that make up a set (also known as the set's elements or members) can be anything: numbers, people, letters of the alphabet, other ...
0
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1answer
21 views

Convention for 2-Space and 3-Space

I am curious by this following symbol which I see on the Math.SE alot which is the following: $$\mathbb{R}^2 \ \mathrm{or} \ \mathbb{R}^3$$ This this a convention to write 2-space or all reals 2-...
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2answers
49 views

Ring theory convention

Given $0$ in the integers, and a member $r$ of a ring $R$, is it a convention that the following is satisfied: $0_{\mathbb{Z}}r=0_R$? Note ($r+r+r+...+r$ (n times) is defined to be $nr_1$, where $n$ ...
2
votes
3answers
101 views

$\pi i$ or $i \pi$? [closed]

Is the usage of either $\pi i$ or $i \pi$ technically correct compared to the other? I have seen both used frequently by many sources. Edit: I understand the two are equal. I am asking whether there ...
2
votes
2answers
111 views

Change-of-coordinates and change-of-basis matrices

Consider two basis $\mathcal{B},\mathcal{C}$ of the euclidean space $\mathbb{R}^3$: $$\begin{cases} \mathcal{B} = \{\vec{b_1},\vec{b_2},\vec{b_3}\} \\ \mathcal{C} = \{\vec{c_1},\vec{c_2},\vec{c_3}\} \...
2
votes
3answers
77 views

Should we write $y=mx+c$ as $c + mx$? [closed]

This may seem like a really pointless question but bear in mind I am thinking from the perspective of a school maths teacher. I am recently thinking it would be more intuitive to have a convention of ...
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0answers
20 views

Idempotent operators with higher powers

Idempotent matrices and linear operators are well known in maths and physics, satisfying $O^{2} = O$. Nilpotent operators satisfy $O^{n} = 0$ for some $n \in \mathbb{N}$. I'm wondering if there is a ...
0
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2answers
42 views

What is the convention for binomial expansion?

When doing a Binomial expansion, in general for: $\\(a+b)^n$ Is there a convention for which term you would raise to the power of n first, the a or the b? And does this convention stay or change ...
5
votes
1answer
57 views

Special name for two variables that sum to one?

I'm curious if there is any special name for the variables in the following function: $\alpha+\beta=1$, such that each can be determined by subtracting 1 from the other. Sort of like saying $\alpha$ ...
2
votes
1answer
45 views

Are there standard names for the ends of a homotopy?

In my mind, homotopies have a beginning and an end, a directionality, it is always from something to something. Are there standard names for these in the literature? Can ppl be expected to understand ...
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0answers
96 views

Naming convention for percentages

I have a variable which I've named $TotalRecords$, and another variable which is a subset of $TotalRecords$ which I've named $ExistingFields$ If I calculate $(ExistingFields/TotalRecords) * 100 = x$ ...
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0answers
88 views

What is the “value of an argument of a function” called?

I'm a programmer and therefore used to the differentiate between parameters and arguments. For programmers, parameters are placeholder variables used to store the inputs of functions; arguments are ...
0
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1answer
25 views

Name of Subset of Domain Mapping to Specific Subset of Image

Suppose I have a function $f: X \to Y$, and I choose some subset $Y' \subset Y$. Is there a name for the set $X'$ such that for some element $e$, $e \in X'$ if and only if $f(e) \in Y'$? For example, ...
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0answers
107 views

Does the Leray-Serre-Atiyah-Hirzebruch Spectral Sequence go under a different name?

This is more of a naming convention question than anything else. I am reading up on spectral sequences mainly from the book Lecture Notes in Algebraic Topology by Davis and Kirk. Now in this book the ...
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0answers
39 views

Sin to the base 0 in windows calculator

In Windows-10 calculator, if I typed Sin(30 degrees) I am getting the answer 0.5 which is correct but it is displaying sin₀(30) = 0.5 My question is why sin has ...
5
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0answers
61 views

Defining the derivative a little differently than usual [duplicate]

This is a quick question, and perhaps a quick answer. What keeps us from defining the derivative, formally, as: $$f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x-h)}{2h}$$? Graphically this would mean that we ...
0
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1answer
109 views

Einstein summation: power confusion

Assuming $n_i = \sum_i n_i$ (Einstein summation). If I write $n_i^2$, does it mean $(\sum_i n_i)^2$ $\sum_i (n_i^2)$ Is there a way to differentiate those two expressions clearly using Eistein ...
0
votes
1answer
202 views

What is the $TT^*$ method?

So I have the following task: Let $T_j f(x)=\int_{\mathbb R}f(x-t)e^{it^3}\psi(2^{-j}t)\frac{dt}{t}$ for $j>0$. Prove that $\|T_j f\|_2\leq\|f\|_2$. Now the hint suggests to use the $TT^*$ ...
3
votes
1answer
50 views

What is the right way to write $(a,b) \in E$ where $a$ and $b$ are elements of the set $E$?

Let $E$ be a set and $a$ and $b$ two elements of $E$. How do you write correctly the previous statment using formal language? Let me explain where my question comes from. When I define multiple ...
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0answers
40 views

Name of induced map

If we have three $k-$vector spaces $V,W,U$, then, for a linear map $T:V\to W$ we have an induced map $T^*:L(W,U)\to L(V,U)$ defined by $T^*(f)=fT$. This map is usually called the transpose of $T$. ...
3
votes
2answers
82 views

“go / goes to” $(x \to y)$ vs. “maps to” $(x \mapsto y)$

Is there a convention for determining when to use $\to$ vs when to use $\mapsto$? Or is there some flexibility between the two? I have only ever seen $\to$ used within the notation for limits (ie I ...
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0answers
52 views

Linear transformation for matrix using Einstein convention [duplicate]

I feel like I am stuck. How can I interpret the equation with Einstein summation? Here is the exercise: you should see that r′ can be written as a linear transformation of r. This means we should ...
0
votes
1answer
52 views

Complex conjugate in inner products

When we solve for inner product of $\rvert a \rangle \cdot \rvert b \rangle$ we solve for $\langle a \rvert b \rangle$ where $\langle a \rvert$ is complex conjugate of $\rvert a \rangle$. However this ...
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0answers
25 views

Terminology: naming different data-set computations / operations types

intro: I'm translating a manual for some 3D graphic utility which modifies set of vertices for a provided set of meshes. So basically it works with sets of sets of vectors. And the thing is - the ...
0
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1answer
63 views

Is the term *monotone* used fairly consistently to mean non-decreasing or non-increasing but not strictly?

In BBFSK, (~1960, Germany) at least in the section I am currently reading, the authors use the term monotone increasing (decreasing) to mean what I often see called strictly increasing (decreasing). ...
1
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1answer
103 views

Does the assumption $0^0=1$ ever lead to a contradiction or conflict with another useful assumption?

There are some places where the assumption $0^0=1$ is formally useful. For example when expressing polynomials $$f\left[x\right]=\sum_{i=0}^{n}a_i x^i.$$ That leads me to question whether $0^0=1$ ...

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