Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [notation]

Questions 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.

Before asking a question on the site, please check if you can find your answer in Earliest Uses of Various Mathematical Symbols or the book A History of Mathematical Notations.

Alternatively, a textbook or paper usually takes the time to explain the notation they're using; please remember to mention where you've seen the notation you are asking about.

12848 questions
78
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2 answers

What does := mean?

What does := mean?
ilhan
  • 973
71
votes
4 answers

Symbol for elementwise multiplication of vectors

This is a notation question. Assume one is given two vector $\mathbf{a}$ and $\mathbf{b}$, and one constructs a third vector $\mathbf{c}$ whose elements are given by $$c_k=a_k b_k$$ Is there any standard notation for this simple operation? Is…
D R
  • 1,158
66
votes
3 answers

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.
Locke
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66
votes
10 answers

Symbol for "probably equal to" (barring pathology)?

I am writing lecture notes for an applied statistical mechanics course and often need to express the notion that something is very probably true for functional forms found in the wild, without launching into a full digression for pathological…
mewahl
  • 719
59
votes
8 answers

How does one denote the set of all positive real numbers?

What is the "standard" way to denote all positive (or non-negative) real numbers? I'd think $$ \mathbb R^+ $$ but I believe that that is usually used to denote "all real numbers including infinity". So is there a standard way to denote the set $$…
dtech
  • 823
53
votes
13 answers

Notation for an interval when you don't know which bound is greater

Is there a notation in English written mathematics for $$\textit{the interval of all points lying between two real numbers $a$ and $b$}$$ when you don't know which of $a$ and $b$ is greater? Which one is greater is completely irrelevant for what I…
Arnaud Mortier
  • 27,276
47
votes
3 answers

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 $\mathbb R - \mathbb Q$?
KeithSmith
  • 1,013
47
votes
7 answers

Symbol for “such that” (not in set)

If $A$ is a set, we can use the set notation $$A= \{ b \mid\text{property $p_1$ of $b$}\}$$ But say $A$ is an element like $b$, $$A = b \mid \text{property $p_1$ of $b$}$$ is this a usual notation? I am trying to say that $A$ is a $b$ that such…
william007
  • 711
40
votes
7 answers

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 "colon equals" sign, where this example is taken from…
Moderat
  • 4,437
40
votes
5 answers

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 contradictory (or unreliable) information. It…
Channel72
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38
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3 answers

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 Tao's blog (4 months ago), I had never seen a…
Gaurav Tiwari
  • 1,541
37
votes
2 answers

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 $\partial \Omega$. This translates to words as the…
John
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37
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5 answers

Is there a sign for 'not less than', 'not greater than', etc.?

I was wondering about this, just now, because I was trying to write something like: $880$ is not greater than $950$. I am wondering this because there is a 'not equal to': $\not=$ Not equal to is an accepted mathematical symbol - so would this be…
Carlos Carlsen
  • 787
35
votes
2 answers

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.... instead of addition...
tekknolagi
  • 541
34
votes
7 answers

How to write \mathcal letters by hand?

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/convenient ways to write out a mathcal D by hand,…
Hugh Perkins
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