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 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 ...
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 ...
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.
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*} ...
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 ...
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, ...
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 ...
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 ...
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 ...
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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: ...
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 ...
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 ...
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 $\hat B=90$ ...
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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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 ...
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 ...
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 ...
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 ...
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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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 ...
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 ...
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 ...
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. $T_pM$...
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 $k$. ...
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 ...