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Questions tagged [convention]

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

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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 ...
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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). ...
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Nth-order Laplacian

Mind that I'm coming from a mostly physics background, so this may in fact be common mathematical notation that I simply haven't come across in my own field. I've seen the symbol $\nabla^2$ "applied" ...
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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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A fixed number or any number

This is a question about the convention. I am confused about whether a symbol means a specific and fixed number or any number. Here is a recent example on the definition of margin for perceptrons (in ...
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When is it appropriate to add a title to a theorem?

I am writing a paper and I have proved a couple of theorems and three propositions. Is it appropriate to add titles to these theorems and propositions for more clarity? For instance, say Theorem 2. (...
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Is there a name for the convergent/divergent status of a series, sequence, or integral? A name for its “behavior” as far as those ideas are concerned?

My professor refers to it as "con-dive behavior", but I'm almost certain that that's not an actual term. For example, he might ask: "what is the condive behavior of the harmonic series?", to which we ...
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50 views

Is the exclusion of infinite decimal expressions of the form $a_0.a_1\dots{a_n}\bar{9}$ logically necessary?

My question really is as simple as: Is the exclusion of infinite decimal expressions of the form $a_0.a_1\dots{a_n}\bar{9}$ logically necessary? The obvious alternative would be $a_0.a_1\dots{a_n}\...
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1answer
54 views

False Proof of $0^0=1$ [duplicate]

I saw the following argument on Quora that provides which should actually be a false proof since $0^0$ is not defined to be $1$. $(a+b)^{n}=\sum_{k=0}^{n}\binom n{ k}a^kb^{n-k}$. Put $a=0, b=1, n=...
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Is there a notation for iterated/repeat concatenation?

Given a string x and natural number y, is there a commonly used notation for a function that concatenates string x to itself y times? Example: $x = \mathrm{'foobar'}$ $y = 3$ $f(x,y)=\mathrm{'...
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Double Supremum Conflicting Conventions

We read $$\sup_{x\in X}(\sup_{y\in Y} f(x,y))$$ left to right (there's really no other choice), but Question 1: doesn't this contradict the following conventions? Stuff inside parentheses is ...
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Should $d/dx$ ever be used when solving for a partial derivative? Or would all instances of it be replaced with $\partial/\partial x$?

You hold one of the variables constant and find the derivative of the other when trying to find the partial derivative, so wouldn't something like this be correct?: $\frac{\partial}{\partial x}(|xy|) ...
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Do the $|$ around $|\langle u,v\rangle|$ refer to absolute value in the inner product version of the Cauchy-Schwarz inequality?

The full inequality is: $|\langle u,v\rangle| \leq ||u|| ||v||$ I understand that $||$ around the vectors $u$ and $v$ signifies the taking of their norm, but what do the single | around $\langle ...
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Looking for a proper math notation to deal with intervals

Say we have two sets like this: $A = \{a_1,a_2,a_3,a_4,a_5,a_6,a_7,a_8,a_9,a_{10}\}$ and $B = \{b_1,b_2,b_3,b_4,b_5,b_6,b_7,b_8,b_9,b_{10}\}$ I want to be able to build something like this: $[(a_{1},...
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3answers
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Need help understanding variable label/scoping rules for first order logic

I don't understand when we're allowed to use what label when we're writing a proof in first order logic. During $\forall$-intro we introduce a new variable $c$ and then close out with something in ...
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Why is it a convention to use gamma to denote a curve?

Why is it a convention to use $\gamma$ to denote a curve? (This is a meta question, but I couldn't find a "meta mathematics" stackexchange, so I'm trying here.)
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Convention: A degenerate cuboid is a rectangle; is its surface area twice the rectangle's area or only once?

A degenerate cuboid is a rectangle. What about its surface area? Is it twice the rectangle's area or only once the rectangle's area? What is the convention here? The latter is more natural but the ...
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convention in writing measurement results in log-normal distribution

from a physical phenomena with log-normal distribution, someone writes a measurement result as $30 \pm 13 $ cm. How do I know whether they are $\mu \pm\sigma$, $\mu* \pm\sigma*$, $E[x] \pm SD[X]$...
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1answer
22 views

Which logical connective is implied by a semicolon?

In a definition Definition. Proposition P(x) holds if A(x) is true; B(x) is true. Usually I'd expect to see "and" or "or" to connect the two statements. What does the semicolon ";" ...
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Arbitrary area function

If I wish to express the area of any closed curve in $R^2$ as a function, is there a more efficient way to do so than to use integrals. I ask this because, in the case where this closed curve is ...
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1answer
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Fourier Transform Syntax and Conventions Clarification

One common definition of a fourier transform for function f(x) is $$F(v)=\int_{-\infty}^\infty f(\tau)e^{2\pi i\tau v}d\tau$$ I know some definitions have an extra sqrt(2*pi). I shall ignore that. ...
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Naming convention for matrix that is not inverted [closed]

There is the inverse matrix, but how do we call the matrix before it became a inverse matrix? I called it normal matrix before but it sounds confusing cause normal makes it sound that it has to do ...
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The right way to calculate the tuples of Permutation

I was studying Permutation in a 'Groups' class. They thought me that the multiplication of two tuples $\alpha\beta=(1\,2\,3)(2\,4\,1\,3)$ in $S_5$ is defined as following: $$ \alpha\beta(1)=\alpha3=...
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Is there a difference of sign conventions of Dirac Index between mathematics and physics?

In section 12.6.2 of Nakahara, on a four dimensional manifold, the index of a twisted Dirac operator is given by $$\mathrm{Ind}(D\!\!\!\!/_{A})=\frac{-1}{8\pi^{2}}\int_{M}\mathrm{Tr}(F\wedge F)+\frac{...
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1answer
28 views

Why are transformations always on the left side of the object?

I'm doing some philosophy involving time evolution operators. Thus I might have two operators $A$ and $B$ which operate in order on the state of the world, $x$. This might be written mathematically ...
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1answer
56 views

Do we really mean “Cartesian Product of Vector Spaces” or is this just a naming convention?

While approaching tensors, I faced what is considered to be the cartesian product of 2 vector spaces. Now as much as I understood what this practically mean, I was quite concerned by its definition. ...
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38 views

Is use of arrows between equations recommended

In high school, I was told that I always should use arrows to indicate rearrangements of equations, such as: \begin{eqnarray} a\left[b+\frac{c}{d}\right]&=&a\\ &\Updownarrow&\\ 1-\...
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Best practice or convention for ordering functions in product

Is there a convention for the order of functions in a product? Obviously order doesn’t matter in a product, I am mainly referring to ästhetics. For example, should trig function go first before ...
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Is there a standard way to view a field $k$ as a $k[x]$ module?

This is a question about mathematical convention. Is there a standard way to view a field $k$ as a $k[x]$ module? My guesses for a "most standard" candidate would be to set $x$ to be evaluated at $1$...
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37 views

Operator precedence in addition and subtraction

Customary operator precedence has addition prior to subtraction. Apart from historical convention and notational consistency, is there a rationale for this?
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37 views

Convention for $(-1)^x$ in closed form expressions ($x\in \Bbb{R}$)

I'm trying to find the closed form expression from a question but I'm debating whether I should include $(-1)^x$ in it, which would make the question significantly easier. My problem with the question ...
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Convention for symbol denoting a generic scalar quantity?

Is there a convention for a symbol to denote any generic scalar? Somehow I have in the back of my head that one would use $\lambda$ for that, but I cannot find any examples now.
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How can I express a single item in a set that meets a certain condition?

For example, how would I show that a variable is equal to a single item in a set which meets a certain condition? Is set builder notation the best way? E.g. $b = \{a \in A | f(a) = 3 \}$ The reason ...
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What conventions are there for notating graph labels?

So I'm writing a paper and I want I often find myself needing to somehow notate the label of a vertex or edge. For example I may need to write some condition that determines if a vertex in a graph ...
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Product Notation Conventions

If a product has the following notation, does that mean the product has zero terms? If there is an expression after this symbol, is the entire quantity, with the product symbol included, equal to zero?...
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Special name for $k!\binom{n}{k}=\frac{n!}{(n-k)!}$

$$\binom{n}{k}=\frac{n!}{k!(n-k)!}$$ The expression above is also known as binomial coefficient. Is there a similar naming convention that describes the one below? $$k!\binom{n}{k}=\frac{n!}{(n-k)!}$$
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How to identify principal root or when product of square root is positive or negative?

I understand for example that $x^2=4$ can be $+2$ or $-2$. An example is the following equation: $3+(6m-26)^{1/2}=m$ where $m = 5,7$. When I however substitute $5$ or $7$ in. I don’t know if the ...
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99 views

Kronecker Delta with 3 indices

I want to express some equations in Einstein summation convention to improve readability and possibly simplify the calculations. I have searched for 3-dimensional versions of the Kronecker Delta, ...
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How to determine the scope of a proof?

When given exercises for my coursework, I often encounter the problem of not knowing how pedantic to be in my proofs. Some seem to be statements so trivial that I'm forced to question whether or not ...
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Question regarding notation for semidirect product

When you say that $G$ is a semidirect product of (a cyclic group of prime order) by (a finite abelian group of odd order) does that imply the direction of the symbol for semidirect product (...
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Is it rude to use the phrase “so called” in mathematics?

I have sometimes heard speakers at seminars refer to named theorems or definitions by prefacing them with the phrase "so-called". For example, "the so-called Theorem of Highest Weight. . ." "...
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Is there a name for the sum of the off-diagonal components of a tensor?

If you have a matrix, the "trace" of the matrix is the sum of the diagonal components of the matrix. For example, given a matrix $\mathbf{A}$: $$\mathbf{A} = \begin{bmatrix}a_{11} & a_{12} & ...
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Conventions about z axis

I was doing an exercise to learn about parametrization and I stumbled upon one that I thought had no answer, it asked for the parametrization of the curve formed by the intersection of $z=\sqrt(x^2+y^...
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1answer
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Distinguishing between inner product and outer product in matrix notation

As a recent field transferee from chemist to data scientist, I find myself wading through more matrix multiplication than I'm used to. I did some linear algebra way back, but I struggle with ...
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What is a/b/c/d? That is: What is the correct order for multiple consecutive division operations? [duplicate]

Unlike with addition, subtraction and multiplication where the order of operations will lead to an unambiguous result when the rules of BIDMAS (or PEMDAS) are applied, this does not hold true for ...
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1answer
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Why Krull dimension of zero ring defined to be negative or it is just a convention?

From wikipedia I have accrossed this claim "The Krull dimension of the zero ring is typically defined to be either ${\displaystyle -\infty } $ or ${\displaystyle -1} $. The zero ring is the only ring ...
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1answer
134 views

How to use basis vectors defined as partial derivative operators?

Edit to add clarification and improve notation: This question was originally written for physicists, not mathematicians. I have differing expectations of the reader in those different contexts. My ...
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Convention for Expressions Involving Exponents

Is there a reason why positive exponents are preferred in some settings over negative? Further, I've noticed if there's a positive rational exponent, then it is sometimes expressed as a product with ...
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2answers
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Empty Cartesian Product, what is $\mathbb{R}^0$?

What is $\mathbb{R}^0$? More specifically, I assume, the Cartesian product: $$\prod_\emptyset \mathbb{R}.$$ Is there a convention here? I ask because I've stumbled across a definition in topology ...
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Variable introduction convention to reduce redundant terms

Is there some guideline or mathematical norm for when to introduce new variables in order to reduce redundancy in an expression or equation? Say I have the function: $S(n)=a\left(\frac{\left\lfloor\...