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

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3
votes
8answers
241 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 ...
10
votes
3answers
789 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?
29
votes
11answers
5k 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 ...
2
votes
3answers
463 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) ...
0
votes
1answer
44 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 $\lambda_g(x)?$ ...
2
votes
2answers
283 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.
4
votes
3answers
105 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 $X_i$ ...
0
votes
1answer
176 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 ...
1
vote
1answer
160 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 ...
2
votes
1answer
69 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 ...
1
vote
1answer
50 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 ...
1
vote
2answers
54 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 ...
2
votes
2answers
78 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 ...
1
vote
1answer
154 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: $$ ...
2
votes
1answer
258 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 ...
-2
votes
4answers
112 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 ...
0
votes
1answer
253 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 ...
20
votes
6answers
610 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 ...
8
votes
2answers
2k 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 $t$ ...
2
votes
1answer
4k 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 ...
2
votes
2answers
53 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 ...
6
votes
4answers
155 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 ...
0
votes
1answer
222 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 ...
7
votes
2answers
357 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 ...
3
votes
1answer
515 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 ...
4
votes
3answers
702 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 ...
3
votes
2answers
235 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 ...
9
votes
3answers
3k 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 ...
2
votes
2answers
525 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 $[0,\pi]$ ?
9
votes
5answers
655 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\} = ...
0
votes
1answer
34 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 ...
2
votes
1answer
227 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\} | ...
1
vote
1answer
320 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 ...
1
vote
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 ...
6
votes
2answers
196 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 ...
11
votes
5answers
2k 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 ...
3
votes
3answers
389 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 ...
2
votes
2answers
17k 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 ...
1
vote
2answers
102 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 ...
1
vote
1answer
101 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 ...
15
votes
6answers
4k views

No radical in the denominator — why? [duplicate]

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 ...
2
votes
3answers
542 views

Why are there two possible triangles when given SAS?

I gave my trigonometry students the following example: Solve $\triangle ABC\ $ , where AC=0.923, AB=.387, and $\measuredangle A\ = 43.33^\circ\ $. First I found BC using the law of cosines, then I ...