Question on the meaning, history, and usage of mathematical symbols and notation. Please remember to mention where (book, paper, webpage, etc.) you encountered any mathematical notation you are asking about.

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6
votes
1answer
124 views

Bourbaki and set inclusion

Which notation ($\subset$ or $\subseteq$) was preferred by Bourbaki for set inclusion (not proper)? A side question: Was the notation for subset one of the many notations invented by Bourbaki?
5
votes
1answer
32 views

Is there a standard notation for the product from right to left?

I am considering a product of the matrices $(A_i)_{1\leq i\leq n}$ in reverse order $$P=A_nA_{n-1}\dots A_1,$$ and I was wondering if there was a standard notation for it, like ...
0
votes
2answers
51 views

About the definition of fixed-point combinators

I am reading this wikipedia page to understand Fixed-point combinators: In computer science, a fixed-point combinator (or fixpoint combinator[1]) is a higher-order function y that satisfies the ...
6
votes
2answers
122 views

What is the meaning of $\mathbb{R}\setminus\{0\}$?

This is used in many posts related to functions and googling it doesn't help. What does this mean? $\mathbb{R}$ should stand for all Real numbers.
1
vote
1answer
38 views

In set theory, what do the subscripts $A_1,A_2,\dotsc,A_n$ mean? [on hold]

How are subscripts used in set theory, for example, In set theory, what do the subscripts $A_1,A_2,\dotsc,A_n$ mean?
2
votes
2answers
52 views

The mysterious $\dot{H}^{-1}$ notation.

I have encountered the $\dot{H}^{-1}$ notation in one of the SIAM Journal on Mathematical Analysis articles. It appears to be standard (or at least not uncommon) to use this one in the field, since ...
0
votes
0answers
15 views

Notation: column/row projection function for matrix-like objects

If we have a $n$-tuple $\mathscr x$ $$\mathscr x := (x_i)_{i\in n}=(x_0,x_1,\ldots,x_{n-1})\in \prod_{i\in n}X_i$$ where $(X_i)_{i\in n}$ is an indexed family of sets and $x_i\in X_i$. We can ...
0
votes
0answers
20 views

Question about bilinear and quadratics form

I'm reading this book: Geometry of algebraic curves by Cornalba, Harris etc. At page 289 there is an excercise where the authors define a quadratic form $Q:V \times V \rightarrow \mathbb{C}$ taking ...
11
votes
7answers
1k views

Is an empty parenthesis a valid mathematical expression? [on hold]

Is using an empty parenthesis valid? For example, $15+()=15$. What is the meaning if it is valid? I need an academic reference to validate this.
0
votes
1answer
37 views

Math notation clarification

I'm working on learning more about logistic regression and I came across an equation with some confusing notation that I've never seen before: $$ \frac{\delta}{\delta \theta_{y'}^{(j)}} l(\theta) = ...
5
votes
5answers
110 views

Where could (do?) we go after exhausting greek letters?

I'm still in high schools but after all my various math and science classes including calculus, statistics, geometry, and physics, I think that we've pretty much run the course of both upper and lower ...
0
votes
0answers
11 views

Alternative single-letter notations in statistics

I'm learning about statistics, and a thing that is difficult for me is the common use of multi-lettered variables and functions. For instance Standard Error of $\beta$ is written $SE(\beta)$ and the ...
1
vote
1answer
36 views

It is okay to have a conditions in a summation limit that depend on the current value of another summation

this is one of those things that I know how to do in a programming environment but not sure how it translates into mathematics. I'm trying to express a sum so that it is easily visible that certain ...
0
votes
1answer
25 views

Vector notation for shifting the elements of a vector

I'm looking for a suitable notation to express a "shift operator" which shifts all elements of a vector forward and sets the first element to zero, e.g., $$\begin{eqnarray*} (1,1,0,1) & ...
11
votes
1answer
237 views

Is the equation $\phi(\pi(\phi^\pi)) = 1$ true? And if so, how?

$\phi(\pi(\phi^\pi)) = 1$ I saw it on an expired flier for a lecture at the university. I don't know what $\phi$ is, so I tried asking Wolfram Alpha to solve $x \pi x^\pi = 1$ and it gave me a bunch ...
4
votes
1answer
113 views

Multiple integral differential notation

When writing a multiple integral, there is sometimes used a shorthand for writing the differential in the integral. For example in $\mathbb{R}^3$ instead of writing $\mathrm{d}x\ \mathrm{d}y\ ...
1
vote
0answers
53 views

How to write the family of sets whose elements are the sets in a sequence of sets

I am wondering, given a sequence of sets $( X_n )$, how do we write the corresponding family of sets whose elements are the sets in the sequence? Of course, the same question applies to nets as well. ...
11
votes
1answer
317 views

Looking for an approach to mathematical notation wherein the universe is divided into disjoint worlds.

Is there a rigorous approach to mathematical notation wherein the "universe" is divided into disjoint "worlds," and the meaning of notation is world-dependent? This would solve a few pesky problems. ...
1
vote
4answers
65 views

What does $T:V\to W$ mean in vector spaces?

What does the sign $\to $ mean in contexts like: "show $T:V\to W$ is an isomorphism" or "if $T:V\to W$ is a linear transformation"...
3
votes
3answers
66 views

Is there a symbol for “given” in mathematics?

Is there a symbol for "given" in mathematics? For example, for the statement: Each member, $x$, of the integer sequence $f(n)$ equals the sum of the two previous members, $f(n-1)$ and $f(n-2)$, ...
0
votes
2answers
47 views

Use of brackets around the integrand

Quick notation question: When using brackets after an integral sign, should the brackets enclose just the integrand or everything - the integrand and the differential, i.e. is it: $$\int ...
0
votes
0answers
13 views

Questions regarding notation (multiple variables, rounding)

I am calculating the coordinates of the Center of Gravity for a 3D volume using the following pseudocode (where A denotes the dimension length and cogA denotes the COG for that dimension) ...
0
votes
2answers
95 views

Proper convolution notation

What would be the correct way to write down the convolution in "star" notation for these two functions; $h(t)$ and $\delta(t-x)$. $\delta$ is the Dirac delta function. The integral notation should ...
0
votes
2answers
28 views

Scalar notation to vector notation for a system of equations

I have a ($1 \times n$) row vector $\boldsymbol{x}$, an ($n \times n$) matrix $\mathbf{F}$, and an ($n \times n \times n$) tensor $\mathbf{Q}$. I also have a system of equations that reads ...
1
vote
0answers
16 views

Complex exponential argument to a function

In many texts on signal processing, the following notation is used to describe the Fourier transform of a discrete time signal $x$: $$ \hat{X}\left(e^{j\omega}\right) = ...
2
votes
2answers
43 views

Sigma Notation multiple sigma

I'm an engineer students, I want to now the runtime of loop inside loop, I get the calculation in sigma notation like the picture above. Can somebody explain to me how sigma inside sigma can be like ...
0
votes
1answer
72 views

Which one of the following logical propositions is to be preferred?

I'm trying to update the symbolism of Giuseppe Peano's "Arithmetices Principia", to make the translation freely available. Might I ask you, which of the following might be a correct mathematical ...
1
vote
1answer
18 views

How to denote a function of all but one parameter (notation question)

Say I have $n$ variables, $x_1,\dots,x_n$ and $n$ functions $f_i$ such that $f_i$ is a function of $x_1,\dots,x_{i-1},x_{i+1},\dots,x_n$, but not $x_i$. Is there a more compact way of denoting this ...
2
votes
3answers
90 views

What set does $\mathbb W$ denote?

What set does $\mathbb W$ denote? I know this may horribly lack context, but I've seen multiple times on M.SE $\mathbb W$ used in some fairly elementary context I think.
3
votes
2answers
19 views

notation for Sumation of Sumation for only for odd iterations

I need to write a summation in summation whether the inner summation should iterate from one through all odd numbers to the teration of the outer summation which goes from 1 to $\infty$... Something ...
-2
votes
0answers
31 views

What does R[-a,a] represent?

More precisely: $f \in R[-a,a]$. All I could find was related to the symbol $\mathbb R$, but I have never seen it in this particular constellation, and even if it stood for "$\mathbb R$", I wouldn't ...
11
votes
2answers
21k views

multiplication equivalent of the summation symbol

I was curious (even though this is a very amateur question)... what would the multiplication equivalent of sigma (the summation symbol) be? $$\sum$$ I want to do a series of multiplication of ...
0
votes
1answer
32 views

How to notate the final element in a sequence?

I'm having troubles putting this in to words here, but here it goes: If I have a sequence of numbers, called $A$ where $A$ is a sequence of numbers that don't seem to have a pattern, how can I notate ...
1
vote
0answers
26 views

Seeking after notation for two objects equal up to a constant

Sometimes we want to express that two objects are equal up to a constant but there is no need to keep writing out the constant or constants. For example, often times the constant or constants involved ...
2
votes
0answers
29 views

Where can I learn more about the “else” operation / “else monoid”?

(The set of natural numbers $\mathbb{N}$ starts at $0$ for me.) Let $X$ denote a set, and define $X_\bot = X \uplus \{\bot\}.$ Let $\mathbf{else}$ denote the binary operation on $X_\bot$ defined as ...
0
votes
2answers
31 views

$\wedge$ in set builder notation

Wikipedia says to use $\wedge$ in set-builder notation like $\{x \,:\, x > 3 \wedge x \neq 10\}$. However, I prefer to merely seperate predicates by a comma. Which notation is more common?
1
vote
0answers
52 views

What's the difference between $Df$ and $Tf$?

I'm reading Michael Shub's Global Stability of Dynamical Systems. In chapter 4, he defined hyperbolic set and said the splitting $E^s$ and $E^u$ are $Tf$ invariant. So I assume this $Tf$ is the ...
1
vote
3answers
45 views

Help With Notation In Fermat's Last Theorem

The following is the notation for Fermat's Last Theorem $\neg\exists_{\{a,b,c,n\},(a,b,c,n)\in(\mathbb{Z}^+)\color{blue}{^4}\land n>2\land abc\neq 0}a^n+b^n=c^n$ I understand everything in ...
4
votes
1answer
64 views

Need Help Understanding Notation With Functions

Original picture: LaTeX approximation: $$f\color{blue}{\substack{(x)\\x\to\infty}}=\pm\sqrt{\frac{(x^2+x)^3}{\pi}}.$$ What does the notation highlighted in blue mean? I understand that ...
1
vote
2answers
45 views

Can we describe quaternions using bra-ket in quantum mechanics?

For example, the rotation plus translation of a point using the language of quaternions is written as $Q(0,x,y,z)Q^* + T$ where $Q$ is the unit quaternion, $(x,y,z)$ is the point, and $T$ is some ...
1
vote
1answer
22 views

Representing Several IF statements inside a FOR loop in Math Notation

I wish to correctly represent several IF statements within a for loop in math notation. The FOR loop can be represented as: ...
2
votes
2answers
48 views

A list from each element of another?

Sorry to edit this so much at this late stage, but the question and answers are confused so much by my incorrect use of terminology and the such, I feel that I should clear this up. Where $a$ and ...
2
votes
0answers
294 views

Reading mathematical notation

Does there exist any site which can parse a series of mathematical symbols and translate them into english text? For example: For all $N$ of the set $I$...
0
votes
2answers
43 views

How to interpret max(min(expression))??

I am reading this paper: ai.stanford.edu/~ang/papers/icml04-apprentice.pdf Step 2 of section 3 is to compute an expression of the form max(min(expr)). What does this mean? I made a simple example ...
1
vote
0answers
20 views

Notation for the set of all integer partitions

I'm working on a project that involves that set $P = \{\{n_1, \ldots, n_k\} \mid k \in \mathbb{N}, n_i \in \mathbb{N} \text{ and } n_1 + \cdots +n_k = n\}$ of all integer partitions of a number $n$. ...
0
votes
1answer
27 views

How's this inertia called?

Let $E/F$ be an algebraic extension. Let $L_1,L_2$ be algebraically closed fields and $\sigma_1:F\rightarrow L_1,\sigma_2:F\rightarrow L_2$ be field monomorphisms. Define ...
0
votes
1answer
40 views

Equation that defines multi-dimensional polynomial

In two-dimensions a complete n-th degree polynomial is given by $P_n(x,y) = \sum_{k=0}^{n}\alpha_kx^iy^j \qquad i+j \leq k \qquad (1)$ . However, now I am dealing with the following two-dimensional ...
0
votes
1answer
35 views

Meaning of $t \mapsto \phi_t(x)$

The context may well be of assistance: Consider a differential equation $x'=f(x)$. Assume that $f:\mathbb R^n\to\mathbb R^n$ is continuously differentiable. Denote by ...
0
votes
1answer
16 views

Conway polyhedra notation calculator?

I recently read about Conway polyhedra notation, and I want to experiment with it. Are there any programs that take the notation, and output a representation of the shape?
1
vote
2answers
76 views

What does ''$\le$'' mean here?

What does ''$\le$'' mean here? Do you know the meaning of $\le$ in the second last line in the text below? The sequence $0\to N \to M \to M/N \to 0$ is exact, so by Problem 5, the sequence $0 ...