Tagged Questions
0
votes
0answers
12 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 ...
8
votes
3answers
81 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 ...
21
votes
9answers
837 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
42 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
30 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)?$
...
4
votes
3answers
78 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
54 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
67 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
43 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
40 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
41 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
41 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
41 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
$$
Where D is a diagonal matrix and X the all ones matrix:
$$
...
7
votes
2answers
322 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
123 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 ...
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 ...
1
vote
1answer
89 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
145 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
410 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 ...
