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
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Mathematical expression for $n$ largest values in a set

I would like to know how to express mathematically $n$ largest values of a given set $A$. For example: I have an unsorted set $A$ with $100$ values $\in \mathbb{N}$ and want to get a new set $B$ with the $5$ largest values. Thank you in advance!
Chris
  • 181
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What is the equivalent of a diagonal in a non-square matrix or array?

I have a non-square matrix $M$, that looks something like this: $M=\left[ \begin{array} & a & b & c \\ d & e & f \\ g & h & i \\ j & k & l \\ \end{array}\right]$ I would like to refer the cells $M_{ij}$ where $i=j$, like $\{a,e,i\}$ in this case. If…
dimitriy
  • 388
17
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1 answer

How to use a clamp function / median in mathematical notation?

I'm writing some mathematical equations that describe some computations in my program and it's pretty important that it's written correctly. At one point, it clamps or truncates a value, $x$, into the range $[0, 1]$. How would i best denote this in…
Detheroc
  • 273
17
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2 answers

Is there a symbol for potential equality?

Is there a symbol for potential equality? Essentially I'd like to condense: $$ (a = b) \lor (a \ne b) $$ so that I can express the phrase "a may or may not be equal to b". Apologies if my syntax is not entirely correct; I come from a computer…
Jake Petroules
  • 411
17
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4 answers

Is there a symbol for plus and minus as opposed to plus or minus?

I know that you can use $\pm$ for when the answer could be either positive or negative, e.g., $x^2=16$, $x=\pm 4$. But is there a symbol that implies that you use both the positive and the negative values? For example, I want to do something along…
Alex Jones
  • 289
17
votes
8 answers

What is the reason behind the current Order of Operations? (PEMDAS)

After reading through a few other questions I was just asking myself: How was the Order of Operations defined, and why is it this specific order and not a different one? Most of us know things like multiplication/division before…
Katai
  • 353
17
votes
4 answers

Math Symbol for "Where"

Pretty much any math text I've read introduces notation through a similar format of equation-notation or notation-equation form e.g ax+b+c where a = ..., b = ..., etc. or Let a = ..., b = ..., etc. ax+b+c I tend to see the former more and…
Kevin Pei
  • 283
16
votes
2 answers

Definition of $C_0$

This is probably a silly question, but a couple of people that I have talked to have had different responses. Does $C_0$ denote the set of continuous functions with compact support or the set of continuous functions which vanish at infinity?
user1736
  • 8,573
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What does $\propto$ mean?

From this article: $\ldots$a maximum-a-postiori "a maximum-a-posteriori $(MAP_{x,k}^{\,\,\,\,\,1})$ estimation, seeking a pair $(\hat{x}, \hat{k})$ maximizing: $$p(x, k\mid y) \propto p(y\mid x, k)p(x)p(k).$$ What does the symbol '∝' mean in…
user1095340
  • 488
16
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3 answers

What does the notation $[0,1)$ mean?

I am studying the procedure for bucket sort from Introduction To Algorithms by Cormen et al, which assumes that the input is generated by a random process that distributes the elements uniformly and independently over the interval $[0,1).$ What does…
Geek
  • 2,349
15
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3 answers

Mathematical notation for a conditional sum

I'm looking for the correct way to define a sum of all elements in a set that fullfill a certain condition. Example: $$ n(A) = \frac{\sum_{F \in A}{ \begin{cases} A_F\text{ is }\mathrm{NULL} & w_F\\ \text{else} & 0 \end{cases}}}{\sum_{F \in…
aKzenT
  • 287
15
votes
4 answers

Notation problem in integration: write $dx$ or ${\mathrm{d}}x$?

I have a question. When I write the integral of a generic function $f(x)$, do I have to write $$\int f(x) \color{red}dx$$ or $$\int f(x) \color{red}{\mathrm{d}}x \quad ?$$ Why? Thank you!
user36390
  • 311
15
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2 answers

Is there a symbol to mean 'this is undefined'?

Consider a partial function $f$ that is defined only for a few values of its domain (my exact use case is $\delta$ transition functions in automata). One can 'complete' it by saying $$g(x)=0\iff f(x) \text{ is not defined.}$$ Is there a symbol to…
badp
  • 1,256
15
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7 answers

Novice – is there something as noise in an expression in mathematics?

It seems to me a silly question, but I couldn't find the answer. Consider the expression: $\frac{(x^2-1)}{(x-1)}$ If $x = 1$, the result is $\frac{0}{0}$. But we can change the expression to: $\frac{(x+1)(x-1)}{(x-1)} = (x+1)$ than, if $x = 1$,…
calebmiranda
  • 193
15
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1 answer

Mathematical symbol to reference the i-th item in a tuple?

Given a tuple e=(x,y), how do I reference the 2nd item (y)?
akurtser
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