0
votes
2answers
42 views

Combinaision of two functions

Let us denote $X_0 = \{x, y\}$ and $X_1 = \{a, b\}$ two disjoint sets of variables; let us denote $V$ a set of values. I have two functions $f_0 : X_0 \rightarrow V$ and $f_1 : X_1 \rightarrow V$, ...
1
vote
0answers
36 views

problems on define set with polynomials

I'm trying to say set A is the set of nonnegative integers that not of this two forms $3x^2 + (6y-4)x - y\ $ and $\ 3x^2 + (6y-2)x + (y - 1)$, for example: $4=3 \cdot1^2+(6 \cdot1-4) \cdot 1-1\ $ is ...
2
votes
1answer
92 views

Which is the best notation for a sequence?

In a set, the order of its elements is (as far as I know) not important; in a sequence, the order of its elements is important. Which is the notation I should use in order to define a sequence? I ...
3
votes
2answers
135 views

Usage of $\cdot$ in calculus

I often find myself caught in the dilemma of whether or not to use the symbol $\cdot$ in calculus. Take for example, the chain rule: $$\frac{dy}{dx} = \frac{dy}{du}\cdot\frac{du}{dx}$$ Is the ...
0
votes
1answer
47 views

Name and notation convention for “unnormalized probability”

Given a finite set of non-negative numbers $S={s_1,...,s_n}$, we can divide them by a normalization constant $Z$ (i.e. their sum) to get a probability distribution. Then we typically say (and write) ...
2
votes
1answer
45 views

Semidirect product notation convention

I was taught that if $G \simeq H \ltimes K$, then (by convention) $H$ is the subgroup that is normal, but I see on Wikipedia and elsewhere that other people use the convention that the above indicates ...
10
votes
5answers
522 views

What are reasons why some symbols in mathematical logic are not standardized?

Why is so hard to find a standardisation regarding symbolism and/or terminology in Mathematical Logic ? We see again and again students asking if e.g. $\rightarrow$ and $\implies$ means the same ...
1
vote
1answer
48 views

Notation in functions spaces

I'm wondering if there is a convention for the following. Let $g:\mathbb{R}^2\to \mathbb{R}$ be given and u in $C^1(\mathbb{R})$. I'm looking for a notation for $g(x,u(x))$ is in the space of ...
2
votes
1answer
109 views

Category of topological pairs

Is there a standard abbreviation for the category of topological pairs? I have searched for it in vain.
2
votes
1answer
85 views

Why is $m$ used as the variable for slope in slope-intercept form?

I was wondering if you could answer a question I have on slope intercept form of a linear equation. I know its $y=mx+b$, but why is it $mx+b$? Don't get me wrong. I know that $m$ is the slope and $b$ ...
0
votes
1answer
33 views

Value expressions

What is the value of the expression: $\sum_{k=0}^{d}b^{k}\left[\begin{array}{c} d\\ k \end{array}\right]\prod_{i=0}^{k-1}\left(c-b^{i}\right) $ for $ k = 0 $? In particular, what is then the value ...
3
votes
3answers
174 views

$x^{y^z}$: is it $x^{(y^z)}$ or $(x^y)^z$?

Of the following, why is a usually considered true, and for what reason other than "tradition" and "more convenient"? a: ${x}^{y^z} = x^{(y^z)} \neq {(x^y)}^z$ b: ${x}^{y^z} = {(x^y)}^z \neq ...
2
votes
2answers
102 views

Is “iff” the same as equality if each member is a predicate?

"Iff" - if and only if ($\Leftrightarrow$ or $\leftrightarrow$, although the first usually carries a "meta" meaning, something that is not evaluated) - is used in $2x=3\Leftrightarrow x=\frac32$, ...
1
vote
0answers
47 views

decimal digit grouping delimiters

I feel a bit silly having to ask this but I just can't seem to find any resources that give an answer to this. When dealing with decimal values that have a large number of digits to the right of the ...
0
votes
2answers
41 views

Is there a convention for precedence of operators in an additive category?

The laws for an additive category are that there must be a zero object, binary products, that every Hom-set is an abelian group, and that the morphism addition distributes over composition. My ...
1
vote
0answers
57 views

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."
1
vote
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 ...
9
votes
4answers
209 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 ...
29
votes
10answers
2k 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 ...
1
vote
3answers
234 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
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 $\lambda_g(x)?$ ...
4
votes
3answers
97 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
114 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
131 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
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 ...
1
vote
1answer
45 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
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 ...
2
votes
2answers
71 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
74 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
348 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
325 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
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 ...
1
vote
1answer
202 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
183 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
959 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 ...