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.

learn more… | top users | synonyms

20
votes
7answers
6k views

How to write \mathcal letters by hand? [closed]

I have a formula in a paper that I want to write out by hand, and it contains two "D"s, a normal D, $D$ in latex, and a 'mathcal', caligraphic D, $\mathcal{D}$ in latex. What are some common/standard/...
20
votes
3answers
714 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 ...
19
votes
10answers
3k views

Entering math through the side door [duplicate]

I am not really good at math, I'd say I'm a lot worse than good when it comes to math but I am a programmer so I have to learn to get over that fact. A lot of times if I want to implement some code I ...
19
votes
10answers
3k views

Why are equations written by equating something to zero?

A linear equation is $$ ax + b = 0 ; \,\, \,\, a\neq 0 $$ A quadratic equation is $$ax^2 + bx + c = 0 ; \,\, a\neq 0 $$ And so on... Why are all these equations written as $\dots = 0 $? Why do ...
19
votes
6answers
13k views

What software and/or language to use to take Math lecture notes? [closed]

I have a terrible hand-writing and I'm very good at typing, so I had an idea about taking my math lecture notes using a computer. I've tried using a simple syntax (using purely ASCII) but it's ...
19
votes
1answer
291 views

$\sin$ vs. $sin$ - history and usage

One thing newcomers to TeX or MathJax often get wrong is that they write something like $sin(x)$ instead of $\sin(x)$ - the point being that common mathematical functions with names consisting of ...
18
votes
6answers
4k views

How to represent “not an empty set”?

I'm writing a academic paper and need to represent "A is not the empty set". What is usual way for professional mathematicians? My idea is: $|A| > 0$ However, using the emptyset $\emptyset$ ...
18
votes
4answers
2k views

Is there a way to denote the calculation $1+2+3+\dots+n$? [duplicate]

Since $n!$ represents $$1\cdot2\cdot3\cdots n,$$ I am wondering if there is a way to represent $$1+2+3+\dots+n?$$ What are some usual notations for the computation of some common sequences? Any other ...
18
votes
2answers
38k views

Weird E letter? (sigma) [duplicate]

Possible Duplicate: What does the math notation $\sum$ mean? My school's prescribed book uses the weird letter E character without explaining what it is in the first chapter when it talks ...
18
votes
4answers
725 views

How to explain this quirk of the chain rule?

Assume I have a function $f = f(y, \phi(y,x))$ and I want to calculate $\frac{\partial f}{\partial y}$, I use the chain rule to get \begin{equation} \frac{\partial f}{\partial y} = \frac{\partial f}{...
18
votes
2answers
2k views

The Gamma function and the Pi function

I have been studying differential equation, in particular special functions. Euler's Gamma function, and Gauss's Pi function are essentially the same, differing only by an offset of one unit. for $...
17
votes
9answers
2k views

Is there an interval notation for complex numbers?

Just as $$\{x \in \mathbb{R}: a \leq x \leq b\}$$ can be written in the more-compact form $[a,b],$ is there an analogous notation for $$\{z \in \mathbb{C}:z=x+yi, x \in[a,b], y \in[c,d]\} \quad ?$$ ...
17
votes
6answers
2k views

Why do we (mostly) restrict ourselves to Latin and Greek symbols?

99% of variables, constants, etc. that I run into are named for either a Latin character (like $x$) or a Greek character (e.g. $\pi$). Sometimes I twitch a little when I have to keep two separate ...
17
votes
6answers
4k views

How many digits does the integer zero have?

Should zero be classified as having no digits, or 1 digit?
17
votes
5answers
1k views

Notation Question: What does $\vdash$ mean in logic?

In a "math structures" class at the community college I'm attending (uses the book Discrete Math by Epp, and is basically a discrete math "light" edition), we've been covering some basic logic. I've ...
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. ...
17
votes
10answers
1k views

Challenge: Demonstrate a Contradiction in Leibniz' differential notation

I want to know if the Leibniz differential notation actually leads to contradictions - I am starting to think it does not. And just to eliminate the most commonly showcased 'difficulty': For the ...
17
votes
6answers
9k views

Contradiction! Any Symbol for?

Perhaps, this question has been answered ago but I don't aware of its existing answer. Is there any international icon or symbol for showing Contradiction or reacing a contradiction in Mathematical ...
17
votes
4answers
2k views

Notation question: Integrating against a measure

Suppose $\mu$ is a measure. Is there any difference in meaning between the notation $\int f(x)d\mu(x)$ and the notation $\int f(x) \mu(dx)$? Many thanks.
17
votes
4answers
898 views

How to write $\aleph$ by hand

So far, I've only seen the symbol $\aleph$ in its printed form and am wondering how this symbol could be written by hand on paper or on a board (in mathematical contexts, of course). Whenever I try to ...
17
votes
3answers
24k views

Is there an accepted symbol for irrational numbers?

$\mathbb Q$ is used to represent rational numbers. $\mathbb R$ is used to represent reals. Is there a symbol or convention that represents irrationals. Possibly $\mathbb R - \mathbb Q$?
17
votes
2answers
35k 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 terms.......
17
votes
5answers
2k views

When should I use $=$ and $\equiv$?

In what context should I use $=$ and $\equiv$? What is the precise difference? Thanks! (I wasn't sure what to tag this with, any suggestions?)
17
votes
1answer
8k views

What's more common? Re / Im or Fraktur-R / Fraktur-I for real / imaginary part?

Title says it all. What's more common? Is there one to prefere (maybe due to some norm)? This: $\operatorname{\mathfrak{R}} z, \operatorname{\mathfrak{I}} z$ or that: $\operatorname{Re}z, \...
16
votes
10answers
3k views

Is there a math function to find an element in a vector?

I would like to write mathematically, if possible, the following statement: Given a vector $x=[1,4,5,3]$ and an integer $j=3$, find the position of $j$ in $x$? How to write this mathematically? ...
16
votes
3answers
4k views

If $\frac{dy}{dt}dt$ doesn't cancel, then what do you call it?

I have $y$ is a function of $t$. I have reached a situation here where I need to evaluate $$\displaystyle \int_0^b{\frac{dy}{dt}dt}$$ Now clearly $y$ has dependence on $t$, otherwise $\displaystyle ...
16
votes
1answer
1k views

$\arcsin$ written as $\sin^{-1}(x)$

I know that different people follow different conventions, but whenever I see $\arcsin(x)$ written as $\sin^{-1}(x)$, I find myself thinking it wrong, since $\sin^{-1}(x)$ should be $\csc(x)$, and not ...
16
votes
5answers
836 views

What are reasons why some symbols in mathematical logic are not standardized?

Why is so hard to find a standardisation regarding symbolism and/or terminology in Mathematical Logic ? We see again and again students asking if e.g. $\rightarrow$ and $\implies$ means the same ...
16
votes
2answers
12k views

What is the difference between kernel and null space?

What is the difference, if any, between kernel and null space? I previously understood the kernel to be of a linear map and the null space to be of a matrix: i.e., for any linear map $f : V \to W$, $...
16
votes
3answers
757 views

Mathematical Notation and its importance

You can see how mathematical notation evolved during the last centuries here. I think everyone here knows that a bad notation can change an otherwise elementar problem into a difficult problem. Just ...
16
votes
1answer
311 views

How and why did Weierstrass $\wp$ get its special symbol?

I kind of always hated drawing the Weierstrass $\wp$ symbol by hand, and it struck me as odd how and why it achieved its special status in the first place. After all, there are tons of other important ...
15
votes
6answers
996 views

Notation of the differential operator

I see the differential operator both with upright and italic d in different books/articles. So I'm curious about $$ \int x^2 \, dx \quad \text{vs.} \quad \int x^2\, \mathrm{d}x,$$ and $$\frac{d}{dx}f(...
15
votes
7answers
1k views

What does $\ll$ mean?

I saw two less than signs on this Wikipedia article and I was wonder what they meant mathematically. http://en.wikipedia.org/wiki/German_tank_problem EDIT: It looks like this can use TeX commands. ...
15
votes
4answers
1k views

Set builder notation, left or right of :| convention

Set builder notation which specify a subset such as $Z$ or $R$ tend to put this condition on the left, whereas other conditions go on the right. $$\{ x ∈ Z : x > 0 \}$$ Why is this preferred over,...
15
votes
6answers
1k views

Appropriate Notation: $\equiv$ versus $:=$

With respect to assignments/definitions, when is it appropriate to use $\equiv$ as in $$M \equiv \max\{b_1, b_2, \dots, b_n\}$$ which I encountered in my analysis textbook as opposed to the "...
15
votes
2answers
12k views

What are usual notations for surjective, injective and bijective functions?

Update: In the category of sets, an epimorphism is a surjective map and a monomorphism is an injective map. As is mentioned in the morphisms question, the usual notation is $\rightarrowtail$ or $\...
15
votes
3answers
4k views

What does this symbol mean? (looks like a 1 with double vertical line)

I'm studying a course on probability and statistics and at some point this symbol comes up without introduction. It looks like the number one, but slightly bigger and with a double vertical line. ...
15
votes
4answers
1k views

Donald Knuth's summation notation confuses me.

I do not understand a lot of cases of Knuth's summation notation in Concrete Mathematics. In general, I cannot seem to get a grasp on the commutative law as applied to manipulating sums. The ...
15
votes
2answers
1k views

What does “∈” mean?

I have started seeing the "∈" symbol in math. What exactly does it mean? I have tried googling it but google takes the symbol out of the search.
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. ...
14
votes
6answers
1k views

In written mathematics, is $f(x)$a function or a number?

I often see notation/wording like "let $f(x)$ be a continuous function" or "let $f(x) \in C^0(\mathbb{R})$". I would say that $\sin$ and $x \mapsto \sin(x)$ are functions, while $\sin(x)$ is a real ...
14
votes
3answers
2k views

Is it possible to write a number in a base of less than 1?

Following on from this question: http://math.stackexchange.com/a/217112/45127 If we take base 10 as an example, the granularity is 1. I.e. we increment the digits in an increment of 1 until we ...
14
votes
3answers
2k views

Symbol for unknown relation?

When solving equations like $$\begin{align} 4x-4 &=\frac{(2x)^2}{x} \\ -4 &= \frac{4x^2}{x} -4x \\ -4 &= 4x -4x \\[0.2em] -4 &= 0\end{align}$$ using the equality-symbol feels like ...
14
votes
5answers
17k views

'mod' or 'remainder' symbol valid in maths?

I am trying to write the Euclidean algorithm in the following way: $A = \lfloor A \div B \rfloor \times B + (\text{remainder of}) \: A \div B $ Now is there any symbol I can use to say "remainder ...
14
votes
5answers
9k views

Backwards epsilon

What does the $\ni$ (backwards element of) symbol mean? It doesn't appear in the Wikipedia list of mathematical symbols, and a Google search for "backwards element of" or "backwards epsilon" turns up ...
14
votes
5answers
2k views

Usage of dx in Integrals

All the integrals I'm familiar with have the form: $\int f(x)\mathrm{d}x$. And I understand these as the sum of infinite tiny rectangles with an area of: $f(x_i)\cdot\mathrm{d}x$. Is it valid ...
14
votes
3answers
2k views

What do $\{ceps_q\}_{q=0}^Q$ and $\{a_q\}_{q=1}^p$ mean?

As a programmer who hasn't had any higher mathematical training, I sometimes find mathematical equations described in books or online that I'd like to implement in my programs, but they have symbols ...
14
votes
3answers
8k views

How did the square root get its shape?

I was wondering when in history did people start use the $\sqrt{}$ sign for square root, what did they use before, and why this curious nomenclature is adopted.
14
votes
4answers
13k views

Representing IF … THEN … ELSE … in math notation

How do I correctly represent the following pseudocode in math notation? EDIT1: Formula expanded. EDIT2: Clarification. (a,b) represents a line segment on a 1D line. a <= b for each segment. The ...
14
votes
4answers
756 views

Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$

In this thread, the question was to find a $f: \mathbb{R} \to \mathbb{R}$ such that $$f(f(x)) = f(x) + x$$ (which was revealed in the comments to be solved by $f(x) = \varphi x$ where $\varphi$ is ...