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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2
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0answers
902 views

History of mathematical symbols, especially the symbol for right angle

Yesterday a child asked me, why (historically) a right angle is denoted by an arc and a dot like in this picture: I dont't know it, but I am interested in it too, so I post this question to this ...
6
votes
2answers
415 views

Index notation for tensors: is the spacing important?

While reading physics textbooks I always come across notation like: $$J_{\alpha}^{\quad\beta},\ \Gamma_{\alpha \beta}^{\quad \gamma}, K^\alpha_{\quad \beta}.$$ Notice the spacing in indices. I can't ...
6
votes
1answer
123 views

Difference between X/A and G/H

I am primarily a student of physics and am trying to self-learn some algebraic topology. I am having some difficulty understanding the differences between the constructions of $(X,A)$ (Pair of ...
4
votes
1answer
794 views

If a matrix is written with a double bar instead of square brackets, is there any significance?

Shilov's Linear Algebra writes a matrix with two bars on each side rather than square brackets. I didn't find any mention of it with a quick Google search, and I can't see any other examples this ...
2
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2answers
335 views

Catalog of named tautologies

Some propositional taulogies have names, for example, Modus Ponens, Modus Tollens, Contrapositon, ... Is there a catalog of all named propositional taulogies? In particular, does the following ...
6
votes
1answer
410 views

Sloppy notation for differential equations

Why does one often use the following notation for differential equation: $$ y'=f(t)y$$ (this is just a particular example) ? What bothers me with this notation, which I have encountered in ...
2
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1answer
93 views

Confusing notation in “Introduction to the Construction of Class Fields”

In "Introduction to the Construction of Class Fields" (by Harvey Cohn) there is this sentence in page 4: "We are hereby asserting that the previous results are all contained in the following ...
2
votes
1answer
634 views

Why are variables lowercased?

While contemplating the existence of math, I came across an interesting problem: Why are variables often lowercased? There may not be a reason, but if there is, I would like to find out. Maybe it's ...
7
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2answers
3k views

What does $\mathrm{Re}(x)$ mean?

I see this all the time in Mathematica output as well as in text, such as near the top of the Wikipedia Beta function page.
2
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1answer
2k views

What does the big cap notation mean?

I'm trying to understand How can an ordered pair be expressed as a set? and I don't know what the big cap/cup notations mean when placed next to an ordered pair: $\bigcap(a,b)$ and $\bigcup(a,b)$.
4
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3answers
2k views

Where can I learn about mathematical notation?

I often see mathematical notation on Wikipedia articles (e.g. Finding the matrix of a transformation). Where is a good resource for learning what the different symbols mean?
1
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1answer
694 views

Functions with subscripts?

In the equation: $f_\theta(x)=\theta_1x$ Is there a reason that $\theta$ might be a subscript of $f$ and not either a second parameter or left out of the left side of the equation altogether? Does ...
1
vote
2answers
317 views

What is the origin of the prefix logic notation used in WFF 'N PROOF?

The classic "modern logic" game of WFF 'N PROOF uses a set of symbols to represent logical relations that I've seen used nowhere else: $C$ for then; $A$ for or; $K$ for and; $E$ for if and only if; ...
2
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1answer
193 views

What is the meaning of a small o in between function names? i.e (f o g)

I am helping with homework. I am stumped here - What is the meaning of the small round circle, or small "o" in question 19 (that I underlined) and question 20
5
votes
2answers
149 views

Can I use $x \in \{a, b, c\}$ to mean that $a, b$ and $c$ are valid solutions?

When solving an equation, can I use the notation $x \in \{a, b, c\}$ to mean that $x=a$, $x=b$ and $x=c$ are all possible solutions to the equation?
3
votes
2answers
91 views

Confusion about a specific notation

In the following symbolic mathematical statement $n \in \omega $, what does $\omega$ stand for? Does it have something to do with the continuum, or is it just another way to denote the set of natural ...
5
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1answer
397 views

idea of the star position in pullback, pushforward notation

i would like to know if there is some idea behind the position of the star in the pullback, pushforward notation or if it is just some notation without background? What's the reason for the star to ...
2
votes
2answers
204 views

Notation of a subset

Is it meaningful to write $U\subset(X,\tau_X)$ where $(X,\tau_X)$ denotes a topological space? Or is it better to write $U\subset X$? Or in fact $(U,\tau_U)\subset (X,\tau_X)$? Thanks!
4
votes
3answers
4k views

Notations involving squiggly lines over horizontal lines

Is there a symbol for "homeomorphic to"? I looked on Wikipedia, but it doesn't seem to mention one? Also, for isomorphism, is the symbol a squiggly line over an equals sign? What is the symbol with a ...
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vote
1answer
313 views

What are notations to express uniqueness in formulae and diagrams?

I am familiar with the notation $\exists\,!$ to express both existence and uniqueness. For example $$\;\;\exists\,!x\!:\!P\,(x)\;\;$$ means "there exists a unique $x$ such that $P\,(x)$ holds", for ...
3
votes
2answers
207 views

Questions about notation $\forall$ and $\exists$

I had a few questions about notation $\forall$ and $\exists$. I am posing each of the question for the former, but I have the corresponding question for the latter as well: 1) If I have only one ...
3
votes
2answers
584 views

Solving tricky Knuth Up Arrow Notations

How would I solve something like $2\uparrow\uparrow n$? when n ≤1? Or $2\uparrow^{-2}2$? Thanks!
3
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5answers
2k views

What does the exclamation mark do?

I've seen this but never knew what it does. Can any one let me in on the details? Thanks.
3
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3answers
385 views

notation for real matrices

Is this a valid notation for real $m \times n$ matrices: $\mathbb{R}^{m,n}$. $m$ and $n$ are known. If it is not, then what would be the right notation for the set of such matrices?
2
votes
0answers
290 views

Why are superscripts used instead of subscripts in this example?

A snippet from Marcus du Sautoy's The Number Mysteries, Chapter 3, in the section called HOW GOOD ARE YOU AT RANDOMNESS is shown below. My question is, why does the author use superscripts instead of ...
5
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2answers
2k views

Advice for how to learn more advanced math for audio signal processing?

I am very interested in learning about audio from a signal processing standpoint. However, whenever I try to further my education by reading books, I get extremely frustrated because the books use ...
17
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3answers
631 views

How to answer a student objection to the use of “of” in pronouncing f(x)?

Once upon a time in elementary school, a student learned how to translate certain English words into math. For example, 'and' usually means 'plus' such as "If John has 3 oranges AND 5 apples, how ...
0
votes
3answers
1k views

What does this notation mean: $\lg^{\ast} n = \min \{ i \ge 0 \,:\, \lg^i n \le 1 \}$?

For my algorithms course I am studying the definition of the iterated logarithm function (and functional iteration in general) and I don't quite understand the set notation used (it's been quite a few ...
2
votes
1answer
324 views

How do you choose names for functions/operators/sets?

Maybe the question will be closed since it's quite informal, however I just try it. Last time I started to suffer from the boundness of the latin alphabet: I need to make the name of the function ...
3
votes
3answers
200 views

Notations about multiple integrals

I have the following sum: $$ S = \int f_1(x_1) dx_1 + \int f_2(x_2) dx_2 + \int f_3(x_3) dx_3 $$ Letting $x = (x_1,x_2, x_3)$ and $f = (f_1(x_1), f_2(x_2), f_3(x_3))$ can I rewrite $$ S = \int ...
2
votes
1answer
189 views

Is $O(10^{-6})$ an acceptable notation in numerical analysis?

In mathematics, the big $O$ notation is used to describe the limiting behavior of a function. It is abuse of notation to say $$ f(x)=O(g(x)). $$ But this is understandable. However, in the class of ...
1
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1answer
332 views

Is it legal to move the vertical bar in an augmented matrix?

Say I am solving a system of linear equations using Gauss reduction. I have got it to this point: $$\left[\begin{array}{ccc|c} 1 & 0 & -1 & 1 \\ 0 & 1 & 1 & 0 \\ 0 & ...
3
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1answer
81 views

Which side should the “hat” of unit vectors point to?

I'm not sure whether to post this here or on TeX.SE. If it belongs there, please move it. When working with unit vectors in physics class, we usually write them with an upside down hat, like this: ...
1
vote
1answer
162 views

Why is it wrong to express $\mathop{\lim}\limits_{x \to \infty}x\sin x$ as $k\mathop{\lim}\limits_{x \to \infty}x$; $\lvert k \rvert \le 1$?

Why is it wrong to write $$\mathop{\lim}\limits_{x \to \infty}x\left(\frac{1}{x}\sin x-1+\frac{1}{x}\right)=(0k-1+0)\cdot\mathop{\lim}\limits_{x \to \infty}x,$$ where $\lvert k \rvert \le 1$? And, as ...
4
votes
1answer
6k views

Subtraction of elements in sets

Let A be a set of finite elements. $A=\{1,2,3,4,5\}$ If I want to remove one element and show I removed one element, how should I do? Pseudo mathematical notation: $A - \{2\} = \{1,3,4,5\}$ Thank ...
1
vote
0answers
123 views

Style guide for the use of '$( \ )$' versus '$[ \ ]$' in mathematics?

I'm wondering if there is any definitive style guide for writing mathematics. In particular, I'm looking for rules for when to use '$( \ )$' versus '$[ \ ]$.' For instance, when referring to a ...
1
vote
1answer
112 views

What does $\stackrel{\mathcal L}{=} $ mean?

I guess $ A \stackrel{\mathcal L}{=} B $ means $A$ and $B$ hand side has the same probability distribution. Is that right?
4
votes
3answers
704 views

Proving that $2n^2+3n+1=O(n^2)$

For Big-O notation in mathematics, How does $f(n) = 2n^2 + 3n + 1 = O(n^2)$? Does it require any more information for the proof? Edit: ...
2
votes
1answer
114 views

Functors preserving (commuting with) exponentials

I have been unable to find any established names for functors preserving exponential objects in general ($F$ such that $F(A^B) \cong FA^{FB}$) and/or those "commuting" with functors $-^A$ (some ...
0
votes
1answer
239 views

Database for mathematical syntax

I sometimes encounter strange mathematical syntax like ${}_n\complement_k$ for $n\choose k$, or $x^{\bar k}$ which is defined as $\Gamma(x+k)/\Gamma(x)$. Is there any good resource where one can look ...
4
votes
2answers
315 views

Is there a meaningful distinction between “inclusion” and “monomorphism”?

The title pretty much says it all. As far as I can tell, the terms "inclusion" and "monomorphism" are equivalent. (Ditto for $\hookrightarrow$ and $\rightarrowtail$.) Is this the case? Edit: ...
2
votes
4answers
1k views

what is ≡ operator equal to in math? [duplicate]

Possible Duplicate: When should I use $=$ and $\equiv$? I heard about this in our calculus class years ago. I was actually not in that class when the processor explained this. 95% of ...
2
votes
1answer
309 views

variable update operator , using “correct” mathematical notation

In a text describing mathematically an algorithm, there is a vector $y_l$ (local y-axis) which is computed, but must be subsequently adjusted to avoid numerical drift. I've considered a few ...
8
votes
6answers
1k views

Some math symbols seem useless

I just noticed that the Unicode character set contains an entire block (256 characters) of math symbols. I also noticed that some of them, don't seem very useful. For example: U+22DA (⋚) and U+22DB ...
8
votes
2answers
535 views

Difference between $:=$ and $=$

I am sorry if this is quite elementary question. But I always think, that why we use $:=$ at some places, instead of $=$. Is there any fundamental difference between these two? Before reading Terry ...
2
votes
1answer
303 views

Sum and subtraction with sets and matrix with formal notation

Hello I have some problems with formal notations, I have to sum (do the union?) of two sets and the sum (union?) of a set and a row of a matrix, is this notation correct? 1) Imagine $T_1 = \{1,2\}$ ...
2
votes
1answer
103 views

Cycle notation question

With $\alpha = (12345)$ in the cycle notation, I should interpret it as: $1\mapsto 2 \mapsto 3\mapsto 4\mapsto 5\mapsto 1$ I need to find out $\alpha^2$ and write it in cyclic notation. As I am not ...
0
votes
2answers
66 views

Validity of the notation $S+\emptyset$

If $S$ is a subset, is $S+\emptyset$ defined and equals to $S$? Or is it just gibberish? Thanks again. 
1
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1answer
57 views

Question on the Range in Limit Notation of an Infinite Sum

I'm studying Knuth's The Art of Computer Programming, Volume 1 (3rd ed.) and came across the following on page 27: The precise meaning of $\sum_{R(j)} a_j$ is therefore $$\sum_{R(j)} a_j = ...
4
votes
3answers
186 views

Linear algebra notation

This is a notation clarification question: If $S$ and $T$ are subspaces of a vector space $V$, is $S+T$ equivalent to $S\cup T$? Thanks.