The convention tag has no wiki summary.
9
votes
3answers
284 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?
20
votes
9answers
596 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 ...
0
votes
3answers
33 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?
$$ \pi(S) = (B, E, C, A, D) \quad and \quad \pi^{-1}(S) = (D, A, C, E, B) ...
0
votes
1answer
29 views
Some questions regarding the convention used
I've some questions regarding the following problem from Herstein. BTW I'm not looking for its solution:
Do $\lambda_g$ is actually $\lambda_g(x)=xg$ when I write $x\lambda_g$ as $\lambda_g(x)?$
...
0
votes
2answers
38 views
Square brackets in indices?
What do these brackets within the indices mean in an equation like
$$ \delta ^\mu _{[\alpha} \eta _{\beta ]\nu} ?$$
I can't find a text, which uses this notation, that explains it.
4
votes
3answers
76 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
50 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
62 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
41 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
37 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
40 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
40 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
39 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
106 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 ...
-3
votes
4answers
93 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
63 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 ...
10
votes
5answers
353 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 ...
3
votes
2answers
128 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 $t$ ...
1
vote
1answer
65 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
45 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 ...
0
votes
1answer
45 views
How is each factor of an expression called?
$$mc^2.$$
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 ...
6
votes
4answers
123 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
55 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
321 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
120 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
2answers
237 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
141 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 ...
6
votes
3answers
523 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
211 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
428 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
27 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
207 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
$$ | \{ x \in o / p^N: x^2 = -1 \bmod p^N\} | ...
0
votes
0answers
81 views
Convention of writing constraint sets
As I will write constraint sets very often, I would like to make sure that I respect the convention.
First, I would like to represent a set of constraints and their relation are conjunction. For ...
1
vote
1answer
51 views
Are segments and intervals always subsets of $\mathbb{R}$?
Which of the following is the accepted mathematical practice?
Any segment $(a, b)$ or interval $[a, b]$ contains only real numbers. If you want all the rational numbers between $a$ and $b$, you ...
5
votes
2answers
143 views
Good Hygiene in using Quantifiers
When using quantifiers it is probably important to pick up certain habits that Veterans agree upon as early as possible.
Since it was pointed out to me by a highly esteemed member that it's ...
8
votes
5answers
388 views
use of $\sum $ for uncountable indexing set
I was wondering whether it makes sense to use the $\sum $ notation for uncountable indexing sets. For example it seems to me it would not make sense to say
$$
\sum_{a \in A} a \quad \text{where A is ...
3
votes
3answers
210 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
805 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
92 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
99 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 ...
9
votes
5answers
1k views
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 ...
2
votes
3answers
313 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 ...
