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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0
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6answers
57 views

What does $\frac{d^2 u}{dt^2}$ mean?

When it comes to taking a derivative, what does $\displaystyle \frac{d^2 u}{dt^2}$ mean ? Does it mean taking derivative of the function twice with respect to $t$. If yes, why is then $d^2 u$ squared? ...
1
vote
2answers
39 views

What does the notation $\int_A$ mean, where $A$ is an event in a probability space?

I am used to seeing integral notation like this, which means the integral over the domain from a to b. $$ \int_{a}^{b} $$ But now I am looking at a statistics book that says "let A be an event" and ...
1
vote
2answers
30 views

Correct to write $\vec{F}:\mathbb{R}^3\rightarrow\mathbb{R}^3$?

Suppose I have some vector field \begin{align} \vec{F}\left(x\left(t\right),y\left(t\right),z\left(t\right)\right)&=G\textbf{i}+H\textbf{j}+T\textbf{k}.\tag{1} \end{align} Would it be correct for ...
1
vote
2answers
29 views

What does $\sim$ in $X\sim \mathcal{N}(\mu,\sigma^{2})$ really mean?

This is a bit of a silly question, but I can't seem to find the answer anywhere. I feel like $X\sim \mathcal{N}(\mu,\sigma^{2})$ means that $\sim$ is a relation, but if it is a relation, what ...
0
votes
0answers
12 views

What does ${\min_{r,s}}{}_{+}$ means? Is it different to ${\min_{r,s}}$?

During my study, I came across these mathematical symbols: $$\delta={\min_{r,s}}{}_{+}\|x_{r}-x_{s}\|, \quad \tau=\min_{r,s}{}_{+}\|\lambda_r-\lambda_s\|,$$ What does $${\min_{r,s}}{}_{+}$$ means? Is ...
0
votes
0answers
9 views

What do these variables in the generic BBP formula mean?

$$P(s,b,n,A)=\sum_{k=0}^\infty \frac1{b^k}\sum_{j=1}^n \frac{a_j}{(nk+j)^s}$$ I would like to understand how this generic type of BBP formula relates to the famous BBP formula: ...
-1
votes
1answer
38 views

Why do people use scientific notation to write very large/very small numbers?

I've seen numbers like these and 10 to the power of any some numbers is used sometimes for very large/very small numbers. Any reason this is used?
0
votes
0answers
11 views

I need a list of conventional symbols for spaces

I often times want to refer to a certain mathematical space, say the space of random variables on $(\Omega,\mathcal A)$ that have a variance, but cannot remember the exact conventional symbol. For ...
0
votes
0answers
28 views

Understanding notation - strange use of the del operator

I'm currently reading a paper with the following notation with the del operator which i have never encountered before: Does $\nabla _m$ just mean $\frac{\delta}{\delta \mathbf m} $ ? Furthermore, I ...
0
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0answers
12 views

Notion of mathematical approximation or tilde symbol [on hold]

I'm trying to read some document that deals with tilde symbols, but I don't know the concept behind it. Could someone please explain it to me in a clear way?
7
votes
3answers
68 views

Pedantic question on function notation and the meaning of domain

Suppose we have a function $f: A\to B$. Then we know, without specifying what $f$ is, that $f$ may or may not map to every element $b\in B$. If $f$ does map to every element $b\in B$ then it's ...
0
votes
0answers
34 views

Basic Function Notation

I had a homework assignment due and I missed this question: $$f(5x) = f(x)^4 + 3 \times f(x) \times f(x)^2$$ with $$f(x) = 2x+1$$ I am really rusty but does this it mean this: $$f(5x) = ...
4
votes
2answers
26 views

When does one use 'succeeds' and when does one use 'greater than'?

I am reading a text on convex optimisation, and there is a line: $f_i(\tilde{x})\leq0$ and $h_i(\tilde{x})=0$, and $\lambda \succeq 0$ and I was just wondering why for one term, $\leq$ is used and ...
1
vote
1answer
28 views

Help understanding a proof about cardinal numbers

I was reading a proof about cardinal numbers, but I do not understand one step. The proof goes as follows: "Let $\beta$ be any ordinal, and for each ordinal $\alpha \lt \beta$, let $\kappa_{\alpha}, ...
2
votes
6answers
58 views

When to use the $\equiv$ symbol (such as in $5^{6}$ $\equiv$ 1 mod 7) vs =

Can anybody explain why we would use the $\equiv$ symbol in the statement $5^{6}$ $\equiv$ 1 mod 7 ? I understand the $\equiv$ symbol means equivalence, but it seems like it would be more appropriate ...
68
votes
6answers
9k views

What did Alan Turing mean when he said he didn't fully understand dy/dx?

Alan Turing's notebook has recently been sold at an auction house in London. In it he says this: Written out: The Leibniz notation $\frac{\mathrm{d}y}{\mathrm{d}x}$ I find extremely difficult ...
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4answers
37 views

what does this symbol mean: [] but without the top bars?

What does the highlighted symbol mean? What are the details of this method?
1
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1answer
48 views

Why sum of two little “o” notation is equal little “o” notation from sum?

Why sum of two little "o" notation is equal little "o" notation from sum? o( f(n) ) + o( g(n) ) = o( f(n) + g(n) ) ? For example: f(n) = n^3 g(n) = 1/n so o(f(n)) = n^2 o(g(n)) = 1/n^2 ...
0
votes
1answer
48 views

What does $k^*/k^{*^2}$ mean?

I'm trying to get a more concrete understanding of what these elements 'look like.' Here $k$ is a field, $k^*$ is multiplicative group, and $(k^*)^2$ consists of the squares in $k^*$.
0
votes
3answers
25 views

Summations and integrals with no upper limits

I've seen expressions like: $$\sum\limits_{i} f(x)$$ And $$ \int\limits_\mathbb{R}f(x)dx $$ What does it mean that they have no upper limits?
0
votes
1answer
16 views

Especifying domain in expressions

When we write things like $\forall x$ does it need to be followed by an $\in \mathbb{A}$ for some set $\mathbb{A}$? Also, sometimes people write things like $\text{for some }x\in(0,3)$: 1)By ...
2
votes
1answer
23 views

Elliptic curve notation

This might be kind of a silly question about notation. I know: $E$: an elliptic curve $\mathbb{F_q}$: finite field But I recently ran across the notation $E/\mathbb{F_q}$ for the first time, so ...
6
votes
2answers
104 views

Is $x_1\cdot x_2\cdots x_n$ proper notation?

In a textbook I recently saw the notation $$x_1\cdot x_2\cdots x_n$$ which was intended to mean $\prod\limits_{i=1}^nx_i$. This is unappetizing to me because for example one wouldn't write ...
0
votes
2answers
55 views

What mathematical idea is the Leibniz notation for derivatives meant to convey?

I know that mathematical notation is often designed to convey some of the mathematical ideas that it expresses -- but I am having trouble getting an intuition for the leibnitz notation like this ...
6
votes
4answers
95 views

What does $\sum_{i=1}^{10} 2$ mean exactly?

Suppose I have $$ \large\sum_{i=1}^{10} 2. $$ Do I just add $2$ to itself $10$ times? I have worked on more complex ones with $n$ and such in the place where the $2$ is, but I have never done it when ...
1
vote
1answer
76 views

Is there a symbol with values 0 and 1 depending on parity of a parameter

Is there a reasonably standard symbol depending on a parameter, like $\delta_i$ or something, that takes the value $1$ when $i$ is even and $0$ when $i$ is odd? or the other way around? $$ \frac{1 + ...
1
vote
1answer
23 views

How should I describe this limiting operation in an equation

In the code I've written, I receive a delta between two position vectors, I then limit this delta by a maximum delta and return the value. To be clear: the direction of the vector remains the same, ...
6
votes
1answer
40 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 ...
8
votes
1answer
279 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?
8
votes
2answers
131 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
42 views

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

How are subscripts used in set theory, for example, In set theory, what do the subscripts $A_1,A_2,\dotsc,A_n$ mean?
0
votes
0answers
21 views

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

If we have a $n$-tuple $\mathscr x$ $$\mathbf{x} := (x_i)_{i\in n}=(x_0,x_1,\ldots,x_{n-1})\in \prod_{i\in n}X_i$$ where $(X_i)_{i\in n}$ is an indexed family of sets and $x_i\in X_i$. We can ...
0
votes
0answers
21 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 ...
0
votes
1answer
39 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) = ...
0
votes
0answers
12 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 ...
11
votes
7answers
1k views

Is an empty parenthesis a valid mathematical expression? [closed]

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
27 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) & ...
0
votes
2answers
48 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 ...
3
votes
3answers
68 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
0answers
14 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) ...
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) = ...
1
vote
4answers
69 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"...
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 ...
1
vote
1answer
19 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 ...
3
votes
2answers
20 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
32 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 ...
0
votes
1answer
36 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
1answer
37 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 ...
1
vote
0answers
27 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 ...
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?