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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3
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3answers
57 views

How to read this expression?

How can I read this expression : $$\frac{1}{4} \le a \lt b \le 1$$ Means $a,b$ lies between $\displaystyle \frac{1}{4}$ and $1$? Or is $a$ less the $b$ also less than equal to $1$? So $a+b$ ...
3
votes
2answers
110 views

What does the notation mean?

Given a measure space $(\Omega,\mathcal{F},\upsilon)$ and a $p>0$. What does the following mean? $$ \|f\|_p=(\upsilon|f|^p)^{1/p}$$
1
vote
0answers
207 views

Notation for drawing a distribution from a constrained distribution

$X$ is a random real variable drawn from a distribution $F$ on the reals, $X \sim F$. In a particular model, the density of $F$, $pdf_F$, is estimated using a collection of points $d$ and a free ...
4
votes
3answers
108 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 $X_i$ ...
1
vote
2answers
4k views

Symbol for the area of a shape

There are mathematical symbols to represent angles ($\angle AB$) and magnitudes ($|AB|$) and what not (ie: not variables, but rather symbol operator thingies). Is there a symbol to represent the area ...
0
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1answer
1k views

What does a dot after a number mean?

So I'm making some calculations for numerical analysis and the output I get in Wolfram or Mathematica for input like: ...
0
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2answers
291 views

Notation for “absolute value” in multiplicative group.

In an additive number group (e.g. $(\mathbb{Z},+)$) there is a well known notation for absolute value, namely $|a|$, which coincides with $\max(a,-a)$, for $a \in \mathbb{Z}$. When the context is a ...
4
votes
0answers
170 views

Mathematical notation for formulas involving trees

I am working on document that requires me to write such things as "$T_1$ is a descendant of $T_0$", or "$N_1$ is an parent of $N_2$". For now, I've been highjacking set notation for use in formulas, ...
2
votes
1answer
207 views

how to write the process of decomposition of a graph into shortest closed sub graphs

If I want to decompose a graph in to possible shortest closed cycles (as shown in right side). then how can i describe this process with mathematical notations. to understand please refer below ...
0
votes
1answer
141 views

Notation $f^{-1}$ for the inverse vs. notation $f^n$ for $n$-fold application

We often use to denote invertible function of $f$, as $f^{-1}$. In applied mathematics, This is the general rule. But very rigorous concepts of mathematics, like axiomatic number systems, it is just a ...
0
votes
1answer
423 views

Mathematical notation of graph subdivision

If anyone can define a directed graph subdivision with mathematical notation, please post a response. My second question is: Irrespective from the planar embedded graph or not, is this definition ...
3
votes
2answers
89 views

Meaning of $ \sup_{n}f_{n}(x)$

What does $ \sup_{n}f_{n}(x)$ mean? In what sense is one function "bigger" than the other? Context: If $\{f_{n}\}_1^{\infty}$ is a sequence of measurable functions, then $ \sup_{n}f_{n}(x)$ is a ...
2
votes
1answer
149 views

What is $\tan^3 x$?

I can't find how to calculate $\tan^3 x$. I don't even know how to use it on a calculator and have no idea what it means. If $\tan x$ is the ascending of the angle $x$, is $\tan^3 x$ the ascending^3. ...
1
vote
1answer
63 views

Notation for the coefficient of the $i$th term of formal power series.

What notation is standard for the coefficient of $X^i$ in a formal power series $P$? I was thinking of $X^i \bullet P$, by analogy with the dot product.
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vote
2answers
11k views

How to Make a Math Symbol in Word

I have a student typing up her thesis. She needs to type external tensor, $\boxtimes$. Is there anyway to get that symbol in Microsoft Word? She doesn't know how to use TeX.
0
votes
1answer
74 views

What do $\mathbb{R}^n$ and $\mathbb{Z}^n$ mean?

If we see the following: $\mathbb{R}^n, \mathbb{Z}^n$, what do they refer to? Thanks.
2
votes
1answer
146 views

in type theory does (x:A) imply ((x:A):A)

In the formulation of type theory I'm reading, (x:A) is an expression of type A. This would seem to imply ((x:A):A) and (((x:A):A):A)... Is this a common feature of type theories? Or am I reading too ...
1
vote
1answer
58 views

How do I write the integral over all $x$ in $\Bbb R^n$?

If I have $f:\mathbb{R}^n\to\mathbb{R}$ I would write the integral over some region $\mathcal{R}\subset\mathbb{R}^n$ like: $$ \int_\mathcal{R}f(\mathbb{x})\mathrm{d}\mathbb{x}. $$ What subscript ...
3
votes
2answers
133 views

$H ≤G$ means $H$ is a subgroup of $G$?

I was reading this page: http://www.proofwiki.org/wiki/Definition:Subgroup I never heard that $H ≤G$ means $H$ is a subgroup of $G$. Is this standard notation ? And if not, what is/are normal ...
8
votes
6answers
2k views

What does the notation $f\colon A\to B$ mean?

I've been doing an online course in discrete mathematics, and the notation $f\colon A\to B$ has come up a few times, and it has not been explained what it means. I tried searching for it on Google, ...
6
votes
1answer
518 views

What are $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$?

Sometimes reading on wikipedia or in this site (and in very different context like topology, arithmetic and logic) I have found these symbols $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$. They are ...
5
votes
2answers
629 views

Why doesn't logic, math, physics etc have a symbol for “example”?

We have symbols for everything but there is no symbol for "example" despite examples being fundamental to achievements. Why is there no symbol for "example" when there are symbols for everything ...
1
vote
1answer
342 views

Name/Symbol for set of combinations without repetition

Given a set $\mathcal{S}=\{1,2,3\}$, I'm interested in the set of all combinations of two elements without repetition: $\{(1,2),(1,3),(2,3)\}$ Is there a name and symbol for such a set? Something ...
2
votes
1answer
238 views

Mathematical notation to describe tiling shapes?

I stumbled across the following Wikipedia article which contained information on tiling by regular polygons. Underneath each image, it contained a sort of sequence of numbers which appears to be ...
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3answers
1k views

Distance between two points

The distance between the two points $P(x_1, y_1)$ and $Q(x_2, y_2)$ is the quantity $$\mathrm{distance}(P, Q) = \sqrt{(\Delta x)^2 + (\Delta y)^2}.$$ Is $(P, Q)$ above indicating an open ...
0
votes
1answer
47 views

Birkhoff Lattice theory notation question- probably easy to answer

In Lattice Theory p. 30 3rd edition: Lemma 3. In any distributive lattice, every polynomial is equivalent to a join of meets, and dually: $p(x_1,...,x_r)=\lor_{\alpha \in A}\{ \land_{S_\alpha} x_i ...
2
votes
3answers
57 views

A question about $[c_0,c_1,\ldots,c_n]$ notation for continued fractions

I try to understand why by definition $[c_0,c_1,\ldots,c_n]=[c_0,[c_1,\ldots,c_n]]$ and also $[c_0,c_1,\ldots,c_n]=[c_0,c_1,\ldots,c_{n-2},[c_{n-1},c_n]]$ . Those are continued fractions, and ...
17
votes
2answers
2k views

Is $A \times B$ the same as $A \oplus B$?

When $A, B$ are $K$-modules, then $A \times B$ is the same as $A \oplus B$. Let $A, B$ be two $K$-algebras, where $K$ is a field. Is $A \times B$ the same as $A \oplus B$? Thank you very much. ...
2
votes
1answer
92 views

Is $\langle f \rangle $ an “inner product”?

Let $$\langle f(x,y)\rangle = \iint_S f(x,y)\,\mathrm{d}x\,\mathrm{d}y$$ I have seen the above in multiple papers as the definition of $\langle f(x,y)\rangle$. I would normally associate angle ...
7
votes
2answers
904 views

Is a bra the adjoint of a ket?

The instructor in my quantum computation course sometimes uses the equivalence $$(\left|a\right>)^\dagger\equiv\left<a\right|$$ I understand that this is true for the typical matrix ...
2
votes
1answer
571 views

Does bra-ket notation work for all inner product spaces?

My quantum computation instructor keeps referring to the vector space in which he is using Dirac's bra-ket notation as an "inner product space", but doesn't it need additional properties to use that ...
2
votes
2answers
67 views

Can minutes be used to measure the length?

I am using an Old American maths textbook and it uses US customary units. For the length, they use minutes (like $6'$ for the altitude of a triangle). How is this related to foot which is the unit of ...
4
votes
1answer
1k views

Indexed Family of Sets

Most books write a family of sets $A_i$ with index set $I$ as $\{ A_i \}_{i \in I}$. However, I've read other books that have criticized this notation; they insist that one should write $(A_i )_{i \in ...
8
votes
2answers
12k views

What does the semicolon ; mean in a function definition

Cauchy's Hypothesis or Noll's theorem states that $\vec{t}(\vec{X},t;\partial \Omega) = \vec{t}(\vec{X},t;\vec{N})$ where $\vec{N}$ is the outward unity normal to the positively oriented surface ...
0
votes
2answers
158 views

Hyperfactorial curiosity

I've been familiarizing myself with the hyperfactorial, and I'm simply curious if it has an extension/analogue into the world of rational numbers, irrational numbers, and complex numbers like the ...
6
votes
1answer
234 views

Is there a rigorous theory of context, whereby sets can gain additional structure within a context?

Consider sets $G$ and $H$ and a function $f : G \rightarrow H$. So far, it doesn't really make sense to ask whether $G$ and $H$ are groups (technically, the answer is "no, they're not groups"), and ...
1
vote
2answers
515 views

How many total order relations on a set $A$?

Let's define a set $T_A$ which is the set of all total order relations on $A$. This set is a subset of the set of all $2$-adic relations on $A$: $$T_A \subset \mathcal P(A^2) $$ 1-Which is the ...
5
votes
3answers
842 views

What do the symbols d/dx and dy/dx mean?

Okay this may sound stupid but I need a little help... What do $\Large \frac{d}{dx}$ and $\Large \frac{dy}{dx}$ mean? I need a thorough explanation. Thanks.
3
votes
2answers
14k views

What does the plus sign contained in a circle ($\oplus$) mean in this case?

The fundamental group of the torus is isomorphic to $\mathbb{Z}\oplus\mathbb{Z}$. I know that the $\oplus$ symbol is the exclusive or symbol but I don't understand how two of the same sets are ...
1
vote
1answer
71 views

Big Oh power difference?

Can a function with higher power like $n^3$ become big oh for a lower power function let say $O(n^2)$
1
vote
1answer
104 views

Big oh and big Omega?

I have question is about big oh and big omega if $f(n)$ is $\Omega(n^2)$ is $f(n)$ $O(n)$?
4
votes
2answers
587 views

Summation/Sigma notation

There are lots of variants in the notation for summation. For example, $$\sum_{k=1}^{n} f(k), \qquad \sum_{p \text{ prime}} \frac{1}{p}, \qquad \sum_{\sigma \in S_n} (\operatorname{sgn} \sigma) a_{1 , ...
6
votes
4answers
344 views

If $f(x)\to f(a)$ when $x\to a$, why don't we denote it as $\displaystyle \lim_{x\to a}f(x)\to f(a)$?

If $f(x)\to f(a)$ when $x\to a$, why don't we denote it as $$ \lim_{x\to a}f(x)\to f(a) $$ instead of $$ \lim_{x\to a}f(x) = f(a)? $$ I need a comprehensible explanation for a newbie like me!
3
votes
2answers
229 views

Tensor notation and rules

I have a few questions about tensors: I appreciate that $g^{\alpha\beta}=g^{\beta\alpha}$ but when contracting say $T^{\sigma}_{\mbox{ }\;\mu\nu\rho}$ to $T_{\;\;\mu\nu}$, first of all can it be ...
1
vote
3answers
142 views

Question about changing a logarithm's base

I've been using the following method to derive/remember the logarithm base conversion formula: If I want to convert $\log_a(x)$ to an expression in base $b$, I say, $$a^{\log_a(x)}=x\\ ...
2
votes
1answer
187 views

A problem with lambda calculus notation and semantics for function-valued functions

I would like to understand how to use the $\lambda$-notation to write usual (set-theoretic) functions, and if it is possible at all. Here are my naïve attempts. Assume that all variables are ...
15
votes
2answers
452 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. ...
0
votes
2answers
238 views

Leibniz notation - how to get $dx$ out of a derivative $v = \frac{dx}{dt}$

I know that velocity equals $v = \frac{dx}{dt}$ which is writen in Leibniz notation. How can i get $dx$ out of it in a proper way? I don't like it when people say that i should just multiply ...
3
votes
1answer
76 views

Does this summation index make any sense?

From my textbook, I have this summation: $$ y_f(k) = \sum_{\tau = k_0}^{k-1}a^{k-1-\tau}g(\tau) $$ So far so good. But then there is a "change of variable" $\tau = \theta - m$ and the summation ...
2
votes
1answer
2k views

In Logic is ⇒, →, and ⊃ basically the same symbol?

I need to create a few truth tables and I got confused by the logic symbols as some of the questions use either one or the other which is really confusing especially if they all mean the same thing. ...