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

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Matrix with rank more than $1$

Is there a shorter way of saying that a matrix $A$ has rank more than $1$? I am looking for something like "full-rank", or "rank-deficient."
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Given a set of rotation matrices, is it possible to determine the rotation conventions employed?

Given three rotation matrices, is it possible to determine the conventions used in defining them? These conventions include: passive or active transformation, pre- or post-multiplication, right- or ...
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1answer
133 views

Where should the 2$\pi$ go in the Fourier Transform?

In some lecture notes on Harmonic Analysis from Terence Tao here, he defines the fourier transform by $$\hat{f}(\tau)=\int_{\mathbb{R}}e^{-2\pi i t\tau}f(t)dt$$ and then says This is really the ...
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0answers
51 views

Canonical way of denoting the set of all (totally) ordered subsets

Given a finite set $S$, we usually denote the set of all subsets of $S$ by $\mathcal{P}(S)$, i.e. the power set of $S$. I need to denote the set of all totally ordered subsets of $S$, let us call it ...
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1answer
34 views

Definition by Recursion and a Question about Induction

I have some questions to ask. Suppose I want to define some sequence of propositional formulas $\{\varphi_{j}\}_{j\in\mathbb{N}}$. First, I define it this way. Fix an enumeration ...
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2answers
55 views

Why do we restrict the range of the inverse trig functions?

I understand why we restrict the domain, but why do we restrict the range? Why do we necessarily care so much for the inverse trig relations to be functions? Thanks!
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5answers
1k views

What type of input does trigonometric functions take in

I see in my Book that 45 deg is equivalent of π/4 . Ι also do the conversion if I simply convert degrees into radians like this 45* π/180 = π/4 radians and ...
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4answers
214 views

Why are the order-of-operations conventions good?

Children are sometimes taught silly mnemonics like "PEMDAS" to remember conventions on order of operations. (I never heard of "PEMDAS" until long after graduating from college, as far as I can ...
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8answers
205 views

What is $2 - 1 + 1$? [duplicate]

$2-1+1$; a fairly straightforward question, but I (well, not me, but Henry Reich) found something strange. Most people would evaluate it as $2+(-1)+1 = 2$; however, this goes against the famed, and ...
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3answers
537 views

Advocating base 12 number system

I had a calculus professor who suggested we should be using base 12 number system. What are the advantages of using such a system?
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10answers
3k views

What could be better than base 10?

Most people use base 10; it's obviously the common notation in the modern world. However, if we could change what became the common notation, would there be a better choice? I'm aware that it very ...
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3answers
249 views

Notation: permutation and its inverse

Consider the sequence $S = (A, B, C, D, E)$ and the permutation $\pi = (4, 1, 3, 5, 2)$: Which of the following is true? $$ \pi(S) = (B, E, C, A, D) \quad and \quad \pi^{-1}(S) = (D, A, C, E, B) ...
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1answer
39 views

Some questions regarding the convention used

I've some questions regarding the following problem from Herstein. BTW I'm not looking for its solution: Do $\lambda_g$ is actually $\lambda_g(x)=xg$ when I write $x\lambda_g$ as $\lambda_g(x)?$ ...
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2answers
140 views

Square brackets in indices?

What do these brackets within the indices mean in an equation like $$ \delta ^\mu _{[\alpha} \eta _{\beta ]\nu} ?$$ I can't find a text, which uses this notation, that explains it.
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3answers
98 views

Notation for $X - \mathbb{E}(X)$?

Let $X$ be a random variable with expectation value $\mathbb{E}(X)=\mu$. Is there a (reasonably standard) notation to denote the "centered" random variable $X - \mu$? And, while I'm at it, if $X_i$ ...
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1answer
121 views

Extend the domain of a function

I get back to a question I post long time ago, because that is quite important to me... Let $\mathbb{X} = \{a, b, c...\}$ be a finite set, $\mathbb{N}$ refers to the set of all natural numbers. I ...
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1answer
135 views

Difference of 2 notations with powerset

Let $\mathbb{N}, \mathbb{V}$ two sets, $\mathcal{P}(\ldots)$ means the power set of a set. $\mathcal{P}({\mathbb{N}})\rightarrow \mathbb{V}$ can be the type of a function mapping a part of ...
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1answer
66 views

Define a domain filter of a function

Let $\mathbb{B}, \mathbb{V}$ two sets. I have defined a function $f: \mathbb{B} \rightarrow \mathbb{V}$. $\mathcal{P}(\mathbb{B})$ means the power set of $\mathbb{B}$, I am looking for a function ...
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1answer
46 views

Name a stable output of a function taking 2 arguments

$\mathbb{C}$ is a fixed finite set, a fair chaotic sequence $(c_n \in \mathbb{C})$ is defined such that $\forall c \in \mathbb{C}, \exists n_0 \in \mathbb{N}, n > n_0 \wedge c_n = c$. That means ...
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2answers
47 views

Notation of functions which get a element of a pair

Given a pair $(a, b) \in A \times B$, I would like to know how to write the functions which get the first element and the second element of the pair... In a programming language, one can write ...
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2answers
72 views

Notation of an iterated function on 2 sets

Let $X$ and $C$ be two sets, I have defined an iterated function on them $f: X \times C \rightarrow X$. What interests me is the iterations of $f$ on an initial value $x \in X$, and a sequence ...
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1answer
76 views

How do you write / represent the 'all ones matrix'?

Is there a convention to write the all ones matrix in formulas? I'm going to write about the following formular: $$ A = B + XD + DX + N $$ Where D is a diagonal matrix and X the all ones matrix: $$ ...
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1answer
185 views

Why is $0^0$ undefined? [duplicate]

Possible Duplicate: Zero to zero power I'm wondering why $0^0$ is considered undefined. Why isn't 1 considered a valid solution? Considering $0^0 = 1$ seems reasonable to me for two ...
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4answers
102 views

Complete instead of Complex, Irregular instead of Imaginary

Will the terms complex and imaginary ever be replaced? At least within beginning classes? I imagine it is more of a kind of hazing into the "mathemitician's club" to allow the terms to confuse ...
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1answer
179 views

Square root principle value convention

Why is the principal square root of a complex number defined as $\sqrt z = \sqrt r e^{-i \varphi / 2}$ for $\varphi \in (-\pi, \pi]$ ? Wouldn't it be more natural to let $\varphi \in [0, 2\pi)$ as it ...
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521 views

Is there a fundamental reason that $\int_b^a = -\int_a^b$

Is there a fundamental reason that switching the order of the limits in an integral results in the negative, i.e., $$\int_b^af(x)\,dx = -\int_a^bf(x)\,dx?$$ As far as I can tell, this is just chosen ...
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2answers
1k views

Obtaining the $\frac{1}{2\pi}$ factor in the Fourier transform

This MathWorld page gives this definition of a Fourier transform: $$F(k) = \int_{-\infty}^{\infty} f(x) e^{-2\pi i k x}dx.$$ But, I wish to speak in terms of linear frequency $\nu$ and time $t$ ...
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1answer
711 views

How to Convert a Number to Roman Numerals

i don't How to Convert a Number to Roman Numerals Using mathematical equation. if M=1000,D=500,C=100,L=50,X=10,V=5,I=1 then how convert any decimal number to Roman Numerals? such as if 1952 then its ...
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2answers
50 views

Name of region defined by two points in higher dimensions

Perhaps this isn't the best place to ask, but I'm trying to figure out the proper name for the region that exists in-between two points in higher dimensions. Under certain conditions, n-cube or ...
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1answer
62 views

How is each factor of an expression called? [closed]

$$mc^2.$$ is called an expression. Correct me if I'm wrong. I'd like to see this expression as $$m * c^2.$$ Here, one of the expression's factors is $m$. Is there a general name for the factors of an ...
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4answers
148 views

Zero polynomial [duplicate]

Possible Duplicate: Polynomial of degree $-\infty$? Today in Abstract Algebra my instructor briefly mentioned that sometimes the zero polynomial is defined to have degree $-\infty$. What ...
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1answer
159 views

Naming conventions for super- and subscripts when naming sets and functions

Ok, so say I want to create a bunch of sets and functions for my to-be paper (that surely will get the attention of those comity members in Stockholm), and I want to identify them with the help of ...
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2answers
349 views

Why does this text insist on changing the variable name here?

In What is mathematics? by Courant, Robbins, and Stewart, "5. An important inequality", the authors change $n$ in this example: $$(1+p)^n\geq1+np$$ to $r$ in this example: $$(1+p)^r\geq1+rp$$ In ...
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1answer
336 views

Convention of digit grouping after decimal point

I read that different cultures have different ways of grouping digits before the decimal point for readability e.g. 1234567890 can be grouped as 1 234 567 890 (English), 12 3456 7890 (Chinese) or 1 23 ...
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3answers
552 views

What is a Neighborhood?

Which of these definitions is more commonly used, and in which contexts? Fix a point $x\in (X, \tau)$. Then a neighborhood around a point $x$ is: a set $N\ni x$ and $N\in \tau$ a set $N$ with $x\in ...
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2answers
221 views

Can mathematical definitions of the form “P if Q” be interpreted as “P if and only if Q”? [duplicate]

Possible Duplicate: Alternative ways to say “if and only if”? So when I come across mathematical definitions like "A function is continuous if...."A space is compact ...
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3answers
2k views

What does a “convention” mean in mathematics?

We all know that $0!=1$, the degree of the zero polynomial equals $-\infty$, the interval$[a,a)=(a,a]=(a,a)=\emptyset$ ... and so on, are conventions in mathematics. So is a convention something that ...
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2answers
449 views

Why is the range of arctan $[ -\frac{\pi}{2} , \frac{\pi}{2}]$?

I've been taught in school and it says on Wikipedia that the range of arctan is $[ -\frac{\pi}{2} , \frac{\pi}{2} ]$. Why isn't it $[0,\pi]$ ?
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5answers
547 views

Set {1,1} = Set {1}, origin of this convention

Is there any book that explicitly contain the convention that a representation of the set that contain repeated element is the same as the one without repeated elements? Like $\{1,1,2,3\} = ...
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1answer
32 views

Notation of instantiating variables by their value in a constraint set

I have a constraint set $C = \{1 \leq x \leq i, j \leq y \leq j+2\}$, now I would like to get another constraint set $C'$ from $C$ to instantiate all $j$ by a value 5, so $C' = \{1 \leq x \leq ...
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1answer
223 views

How many solutions for $x^2 = 1$?

Let $F$ be an non-archimedean local field, let $o$ be its ring of integers, and let $p$ be the maximal ideal Is there a closed form for the cardinality $$ | \{ x \in o / p^N: x^2 = -1 \bmod p^N\} | ...
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1answer
210 views

Convention of writing constraint sets

As I will write constraint sets very often, I would like to make sure that I respect the convention. First, I would like to represent a set of constraints and their relation are conjunction. For ...
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1answer
54 views

Are segments and intervals always subsets of $\mathbb{R}$?

Which of the following is the accepted mathematical practice? Any segment $(a, b)$ or interval $[a, b]$ contains only real numbers. If you want all the rational numbers between $a$ and $b$, you ...
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2answers
187 views

Good Hygiene in using Quantifiers

When using quantifiers it is probably important to pick up certain habits that Veterans agree upon as early as possible. Since it was pointed out to me by a highly esteemed member that it's ...
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5answers
1k views

use of $\sum $ for uncountable indexing set

I was wondering whether it makes sense to use the $\sum $ notation for uncountable indexing sets. For example it seems to me it would not make sense to say $$ \sum_{a \in A} a \quad \text{where A is ...
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3answers
320 views

In what order are chained implications evaluated? (i.e. $a \implies b \implies c$)

Implication does not appear to be associative: a b c | (a -> b) -> c | a -> (b -> c) F T F | F | T F F F | F | T Is $a ...
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2answers
10k views

Square root of a number squared is equal to the absolute value of that number [duplicate]

Possible Duplicate: Significance of $\displaystyle\sqrt[n]{a^n} $? The square root of a number squared is equal to the absolute value of that number. Why is $\sqrt{x^2} = |x|$? Why not just ...
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2answers
101 views

Displaying a reduction of inequalities

This question is about style and typesetting, but I believe it is more appropriate for this site than a TeX site. When a bound is being established for some expression, it is not uncommon to see ...
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1answer
100 views

Instantiate spaces in commutative diagram by “appropriate” elements - name of this idea?

I wonder whether the following concept has a name. Suppose you are given a commutative diagram $\mathcal C$, that we think of a small category where each hom-class (i.e. hom-set) consists of at most ...
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No radical in the denominator — why?

Why do all school algebra texts define simplest form for expressions with radicals to not allow a radical in the denominator. For the classic example, $1/\sqrt{3}$ needs to be "simplified" to ...