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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21 views

What does $\Gamma_\infty$ denote in modular forms

I am catching up on some notes for an online modular forms course. The slides have just suddenly started using the notation $\Gamma_\infty$, without even defining $\Gamma_k$ (except for $k=1$), never ...
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2answers
32 views

Notation question about defining a set

If I'm given: $\{ n^2 + n + 1 \mid n \in \mathbb N\} \subseteq \{ 2n + 1 \mid n \in \mathbb N\}$ Does this mean: "The set $A$ where each element is made by putting a natural number in that formula ...
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1answer
29 views

Split long relation over two line using boolean operator

Normally, when you have a long equation, you can split it on two lines. Suppose that $a$ and $b$ are very long expression. Then, for example: $$ x = a - b$$ can be rewritten as $$ x = a + $$ ...
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1answer
33 views

Shorthand method for expressing the limit of something

Solving limits takes a lot of steps sometimes, but I feel bad leaving out the limit each time I do something and rewrite "=". Is there a shorthand method for writing the limit? $$\lim_{x \to p}f(x) = ...
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1answer
73 views

Simplification of a nested sum

I have a nested sum like so: $$\underbrace{\sum_{k_1=k_0}^{k^*} \ ... \sum_{k_n=k_{n-1}}^{k^*}}_{\text{n times}} 1\quad\ \text{with}\ \ n, k_0, k^* \in \mathbb{N},\ k^*\geq k_0$$ Is there a general, ...
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1answer
41 views

What does the notation $O(x^n)$ mean?

I am reading a book about Padé Approximations, and I am trying to understand the following line: We denote the $[L/M]$ Padé approximant to $A(x)$ by $A(x) - P_L(x)/Q_M(x) = O(x^{L+M+1})$ where ...
2
votes
2answers
28 views

Qualification of a Universal Quantification

Let us say I have a predicate, $P(n)$, and I want to say that it holds for every integer greater than $2$ (an example would be $P(n) = 2n>2+n$). Let us furthermore say that the UOD (universe of ...
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1answer
30 views

Notation for nested sigmas (summations)

Is there any standard notation, other than an ellipsis, for a chain of nested sigma summations? For instance, I have: $$ \sum_{b_0=0}^{L} \sum_{b_1=0}^{L-b_0} \sum_{b_2=0}^{L-b_0-b_1} \cdots ...
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1answer
70 views

What does $\nabla ^\perp$ mean?

As in the title, I am reading a paper and they use the notation $\nabla ^\perp$ without explaining what it means. Is this standard notation for something? I have not seen it before! Thanks in ...
2
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1answer
32 views

$\varepsilon$-neighborhood set notation as $V_{\varepsilon}(a)$ and proof question

Two questions regarding the set $V_{\varepsilon}(a)$. It is defined in the book I am currently using as $$V_{\varepsilon}(a)=\{x\in\mathbb{R}:|x-a|<\varepsilon\}$$ 1). Why the $V$? I suppose ...
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2answers
46 views

Notation of the square root in textbooks

About a year ago, I started to notice that a lot of textbooks of recent date seem to favor the notation $x^\frac{1}{2}$ over $\sqrt{x}$, while I agree that notating the square root as an exponentation ...
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1answer
34 views

Conditioning versus subscripting for a Markov process

I tried to see if this question had been asked anywhere, but it's a bit hard to set up the search terms properly. I want to confirm my a priori notion that the notations $P_{X_\tau}[G]$ and ...
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3answers
45 views

Give the truth table of a single binary connective which is adequate.

This might be a silly question, but I am confused. I know there is a theorem saying the only single binary connectives which are adequate are NOR or NAND, so I could use either of them. And then the ...
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2answers
58 views

Sigma hierarchy of logical formulae

In some papers on mathematical logic I've found references to hierarchy like $\Sigma_1^0$-sentence and so on. What does it mean? What is $\Sigma_n^m$, what is $n$ and $m$ here?
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1answer
34 views

What is P(Y) here?

A multivalued map, f: X -> Y, from a set X to a set Y, is a map f: X -> P(Y). Multivalued maps will be also called multimaps. I don't understand what a multimap is in category theory and I think the P ...
4
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1answer
117 views

The meaning of $\rightsquigarrow$ in math?

In order to write a scientific paper, I would like to use the symbol \rightsquigarrow or \leadsto which look as: $\rightsquigarrow$ or $\leadsto$ I'm wondering about the usual meaning and use ...
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1answer
21 views

How to write a compact list of indices for subsets from finite combinations

I am using the binomial coefficient to calculate the number of 2-outcomes from $n$ items i.e. $\binom{n}{2}$ combinations. I am looking for a way to write the list of combinations compactly in terms ...
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3answers
76 views

Less than or equal sign

If I know for two numbers a and b that $${a < b }$$ Then is it correct to say that $$ a \leq b $$ I know that the second statement is true as long as the first one is. It seems OK as it is ...
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1answer
23 views

How to describe a set of coordinates of variable length?

I need to describe a set of coordinates with up to 8 dimensions. A problem is asking me to describe an event from a experiment involving sampling. The catch is that the experiment doesn't end until a ...
2
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2answers
46 views

Is there a commonly accepted notation for k-subsets?

The question says it all. I have once seen the following notation used for $k$-subsets of a set $S$ but I failed to verify that it is commonly used and I was also unable to find any evidence for a ...
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0answers
21 views

Expressing three recursive forms into one using parameters?

I have the following recursive function that takes three forms and I want to express it in one form: Initial: $f(x) = m * f(x-1)$, $f(0) = value.$ Forms: 1 - $f(t) = m * f(t-1)$. where t is at ...
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1answer
53 views

About a notation in Rudin's “Real and Complex Analysis”

On page 14. Suppose $\{f_n\}$ is a sequence of extended-real functions on a set $X$. Then $\sup\limits_nf_n$ and $\limsup\limits_n f_n$ are the functions defined on $X$ by $$ ...
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3answers
61 views

Function Notation question that needs an answer

$f(x)= f(x+1)+3$ and $f(2)= 5$, determine the value of $f(8)$. I don't understand how $f(x)$ can equal $f(x+1)+3$
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20 views

Mean square convergence notation

Convergence in probability is often stated as lim as n->inf. P(|Xn-X|>e)=0 I am confused because Xn is defined as a sequence of numbers and X as an constant. Isn't the right definition that the ...
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2answers
49 views

Set builder notation

I'm not sure of the correct notation if someone could please help. Say you wish to have a set comprised of the union of two sets, such as $$h=\Big\{ \begin{bmatrix}x & y\\y & x\end{bmatrix}: ...
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3answers
36 views

Notation of this set in a set?

I am currently struggeling with the following notation: For $\epsilon \in (0,1)$ and $p \in (0,\infty)$, consider the following subset of $L ^p$: $M(p,\epsilon)=\{f \in L^p:m \{x:|f(x)| \ge \epsilon ...
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1answer
32 views

Constructing sets involving predicates. Let $P(x),Q(x)$ be predicates over a set $X$?

Let $X$ be a set and $P(x),Q(x)$ be predicates over $X$. Consider the sets $$Y = \{y\in X\mid P(y)\}$$ $$Z = \{z\in X\mid Q(z)\}$$ Complete the following sentences with quantified propositional ...
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2answers
86 views

Can logic and mathematics be used together?

I have been wondering if logical symbols ($\to$, $\sim$, etc.) can be used with traditional mathematical notation ($+$, $/$, etc.) in the same equation. For example, would the following equation be ...
2
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1answer
39 views

How to express MATLAB indexing in math notation?

I am currently writing a paper concerning discrete arrays. Given the following MATALB statement ...
3
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3answers
290 views

What does “$\cong$” sign represent?

I came across this sign when reading some papers. I looked up Wikipedia. It says "The symbol "$\cong$" is often used to indicate isomorphic algebraic structures or congruent geometric figures." So ...
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1answer
48 views

The Mysterious Discrete Math Operator

I am working on some discrete mathematics and came across this strange operator on two sets. $R \circ S$ I have only seen this circle operator with function compositions, so is this "Set ...
3
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0answers
77 views

What symbol expresses “less than approximately”?

Suppose, I want to state that $a$ is less than $b$. However, I do not know $b$ exactly, but only that it is approximately $c$. With other words I want to state that $a$ is lesser than some value which ...
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3answers
80 views

How does ZFC describe addition?

Surprisingly, the Wikipedia article on addition doesn't contain the answer. I looked elsewhere online for it, but didn't find it. Intuitively, the cardinal of the union of two sets seemed ...
0
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1answer
33 views

Is there a way to treat arrays as sets?

I was doing some F.O.L. problems and I noticed that quite a lot of them could be easily solved if I could just treat a given array as a set. Example: $B(1..n)$ is a permutation of $A(1..n)$ The ...
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1answer
15 views

Meaning of Clo(A), Int(A), Rint(A)

I've just stumbled upon this notation in a text about optimalisation with no explanation as to what they mean (suggesting they are widely used and well known?). $A$ is a set (a convex set in this ...
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1answer
40 views

Max(x,y) and argmax(x,y)

I am writing my report and I got confused on this simple maths concept. What I need is: I have 2 values i.e x and y and I want to use the maximum of either x or y as my length. So which statement is ...
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1answer
38 views

Seperation of variables justification?

I haven't found a similar question on Math SE, but I may not have looked enough because I find it hard to believe someone hasn't already asked this. Anyways, here goes: I'm studying mathematics, but ...
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0answers
51 views

What is the Δ above the = symbol?

I am reading this and at equation 4.21 it has an equal symbol with a Δ above it. Do you know how this is called, and what it does? Thanks
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1answer
24 views

How to define a set for a matrix

I have a big matrix and I have partitioned it. So, I want to say that I am taking the summation of entries that do not belong to the blocks in the diagonal. How can I say it mathematically. Is it ...
1
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1answer
35 views

Dot product with scalar equal to common symbol for multiplication

I'm in Algebra 2 now, and for about 3 years I have extensively $$ a \cdot b $$ Instead of $$ a \times b $$ Now, looking into vector math for shaders, I see this is also the dot symbol is also ...
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1answer
42 views

Set notation, what does it mean

Can sonbody explain to me what does set notation of $$ C_NM\\ $$ means. The C in given notation is not letter C, it is some kind of very narrow C. I Could not find the alternative, to write. ...
2
votes
2answers
32 views

Correct notation to indicate multiplying all elements within a set

Is there a correct notation to indicate multiplying all elements within a set? For example, if $M = \left\{n_0, n_1, ..., n_t\right\}$ be the set of elements where I want to multiply all the numbers ...
0
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0answers
30 views

Identity relation of many variables

The identity relation on a set $A$ is $\operatorname{id}_A = \{(x;x) \,|\, x\in A\}$. This can be generalized for any (possibly infinite) index set $N$ as $\{(\lambda i\in N: x) \,|\, x\in A\}$ (here ...
2
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2answers
92 views

What does “\” mean in math

In a Linear Algebra textbook I am reading, the following is stated: $b\notin \operatorname{span}(A \cup \{a\})\setminus \operatorname{span}(A)$. It does so without explaining what "$\setminus$" means. ...
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1answer
48 views

Convention in Riesz representation theorem vs. tempered distribution theory

We are working over the complex field here. Sometimes analysis textbooks say that every continuous linear functional on $L^p$ is integration against some $f \in L^{p'}$ for $p\in (1, \infty)$, rather ...
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1answer
54 views

The symbol $n$? Natural numbers?

This might seem like a very basic question, but it keeps bugging me. Does the symbol $n$ mean the set of natural numbers $\mathbb{N}$ shortened to $n$ to ease writing? Or is it rather the positive ...
11
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1answer
144 views

Why is $e$ the Identity?

Some authors use $e$ to be the identity element of a group instead of $1$. What is the origin of this notation? Was this before or after we used $e$ to represent the base of the natural logarithm? ...
2
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0answers
60 views

Integrating With Respect To $x$

Suppose I have the first derivative of the function $y$, $\displaystyle \frac{dy}{dx} = g(x)$. Furthermore, suppose I want to obtain the function $y$ by integrating with respect to $x$: ...
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3answers
117 views

Equation with the big O notation

How I can prove equality below? $$ \frac{1}{1 + O(n^{-1})} = 1 + O({n^{-1}}), $$ where $n \in \mathbb{N}$ and we are considering situation when $n \to \infty$. It is clearly that it is true. But I ...
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0answers
36 views

Notation for number of tensor permutations

I have a tensor (or set if you will) that consists of N elements, and each element has a limited number of values it can take. For example: ...