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

Which of $\sin^{-1}()$ and $\sin^{(-1)}()$ refers to $\arcsin(\sin(x)) = x$ and $\csc(x) = \frac{1}{\sin(x)}$?
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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 ...
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1 vote
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### 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 $P_k^s(n)$....
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### 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 ...
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 ...
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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 ...
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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 ...
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 ...
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### 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 ...
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1 vote
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### 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 ...
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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 ...
1 vote
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### 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 ...
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### 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 ...
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### 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 ...
1 vote
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### 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 ...
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1 vote
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 ...
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1 vote
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### 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 ...
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