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
7
votes
2 answers

How do you say $3\uparrow\uparrow\uparrow3$?

How do you say $3\uparrow\uparrow\uparrow3$? English is my second language and I'm not sure how I should read it.
GarrettK
  • 73
7
votes
1 answer

Why do they use $\equiv$ here?

I thought I had pretty much figured out the difference between $\equiv$ and $=$. Then I came across this while reading about partial derivatives (in Colley's Vector Calculus): $$ \frac{\partial^2f}{\partial z^2} = \frac{\partial}{\partial z}…
Eivind
  • 1,800
7
votes
4 answers

Math Notation : Is there a clear standard?

Let's take trigonometry as an example We often see $ \theta = \sin^{-1}(x) $ being used to say what is the angle $ \theta$ such that its sine is $x$. But by similar arguments why can't $\sin^{-1}(x) $ mean $\frac{1}{\sin(x)}$ when $\sin^2(x)$ is…
Warren Hill
  • 3,092
7
votes
3 answers

What does $(m, n) = 1$ mean?

I have to solve a problem which states that $(m,n) = 1$, but I have no idea what this means. Maybe, the problem itself will help: Suppose $m, n \in \mathbb{Z}$, with $n > 0$ and $(m,n) = 1$. Show that: $$\left \{ e^{2 \pi i m k/n}: 0 \leq k < n…
Huy
  • 6,674
7
votes
3 answers

What is the correct symbol for "equal-rounded"?

What is the correct symbol for saying "equals, but is rounded"? For example: $$\frac{1}{17}=0.0588$$ Is not essentially correct, since it's rounded. What other equal-like symbol should I use?
Martin Heralecký
  • 335
  • 2
  • 3
  • 10
7
votes
6 answers

Does $x/yz$ mean $x/(yz)$ or $(x/y)z$?

When people write $x/yz$, do they usually mean $x/(yz)$ or $(x/y)z$? For example, from Wikipedia If $p\geq 1/2$ , then $$ \Pr\left[ X>mp+x \right] \leq \exp(-x^2/2mp(1-p)) . $$ Thanks!
Tim
  • 47,382
7
votes
2 answers

Symbol denoting "for at least one"

As a lazy mathematician, I'm tired of having to write "for at least one". Similar to the $\forall$ (for all) symbol, does a symbol exist to denote "for at least one"? I've been abbreviating to f.a.l.o., but I was hoping for some more elegant…
lodhb
  • 681
7
votes
2 answers

How to denote enumerating 1, 2, ..., n?

What is the best way to denote it? $\forall i\in\{1,\dots,n\}: P(i)$; $\forall i=1,\dots,n: P(i)$; $\forall i=\overline{1,n}: P(i)$; $P(i)$ for $i=1,\dots,n$; ...
porton
  • 5,053
7
votes
2 answers

What is the meaning of $\mathbb R^+$?

For a function $f$ that maps set $A$ to $B$, $f\colon\mathbb R^+\to\mathbb R^+$, $f(x) = x^2$ is injective. $f\colon\mathbb R\to\mathbb R$, $f(x) = x^2$ is not injective since $(- x)^2 = x^2$. what is the difference between $\mathbb R^+$ and…
James
  • 1,320
7
votes
4 answers

Confused about notation ":=" versus plain old "="

Relating to sets, I find the following in a text book: "...the set S := {1, 2, 3}". The book has an extensive notation appendix, but the":=" notation is not included. What exactly does ":=" mean, and how is it different from just "=", and how is it…
OldRoboCoder
  • 71
  • 2
7
votes
2 answers

$A^\dagger$ - how to handwrite this?!

In one book I came across the notation $A^\dagger := \overline{A}^T$. But how does one usually handwrite it? When I try to do it, it seems so similar to $A^+$
marmistrz
  • 1,345
7
votes
2 answers

Symbol for set all partitions of a set

Is there a symbol for set all partitions of a set (like P for Power set)? P.S. I need such symbol in writing some mathematical related notes.
Tail of Godzilla
  • 213
7
votes
5 answers

What does $:=$ mean?

What does $:=$ mean? For example: Consider the subset $ \mathbb{S} = \{ p \in \mathbb {P_4} ( > \mathbb{R,R} ) \ | \ P(2)=0 \} $ Suppose $p$, $q$ are in $\mathbb{S}$, so $p(2)=q(2)=0$. Then $r := p + q$ is also a polynomial of degree at most $4$…
Silbol
  • 71
7
votes
1 answer

$\leq$ V.S. $\leqslant$

Is there a substantial difference between $\leq$ and $\leqslant$? My textbook uses both, but I could not tell why the authors selected one or the other. I asked my teacher, and she said that there was no difference between the two, but if there is…
nosyarg
  • 157
7
votes
1 answer

Is a list and an ordered set (or multiset) the same thing in mathematics?

I've wondered whether a list is the same as an ordered set (or multiset) in mathematics ? Since a list can contain the same element more than once, the above can only be true for an ordered multiset ? Sometime people speak about a empty list like it…
Shuzheng
  • 5,533
1 2 3
…
99 100