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

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2
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1answer
242 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
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4answers
110 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
234 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 ...
19
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6answers
596 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
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1answer
3k 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
52 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
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4answers
154 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
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1answer
207 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
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1answer
457 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
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3answers
661 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
234 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
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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
485 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
620 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
282 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
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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 ...
6
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2answers
195 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 ...
9
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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 ...
3
votes
3answers
368 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
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2answers
15k 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
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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 ...
1
vote
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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6answers
3k 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
532 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 ...