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
2
votes
1 answer

Denoting overlapping area in mathematical notation

I have a raster grid and some shapes (see figure below, in which only one of the shapes red is depicted). For each raster cell, I am checking how much of the area of the raster cell is overlapping with any of the shapes. Afterwards, I am multiplying…
Stücke
  • 73
2
votes
1 answer

Is $a/bc$ unambiguous?

In several contributions here on M.SE I saw notations like $$a/bc$$ where from the context one could conclude that it actually meant $a/(bc)$, not $(a/b)c$. Both terms are obviously different in general, and the programming languages I know of have…
emacs drives me nuts
  • 10,390
  • 2
  • 12
  • 31
2
votes
1 answer

Notational question on indexing sets

It's my understanding that if I refer to a collection of sets of the form $A_i$, and refer to the intersection $$\bigcap_{i \in I} A_i$$ for some indexing set $I$, that I am directly implying that the $\{A_i\}$ are countable, which is even more…
John P.
  • 2,136
2
votes
1 answer

Notation question for the set of real numbers

I realize this is probably very specific to the person writing the textbook, but I was wondering if anyone else out there knows the answer. I encountered this in one of my textbooks: $\mathbb{R}_{++}$. Now, I know that $\mathbb{R}_+$ is used to…
user71959
  • 21
2
votes
1 answer

Set of Elements Inside a Curly Brackets with Powers Mathematical Notation

So I am a computer science student and have some problems reading cryptographic mathematics notations, so I need help from mathematicians. I was reading a 2018 IEEE journal about identity-based data integrity checking, and was met with…
rareguy
  • 33
2
votes
1 answer

Meaning of notation $\textbf{1}_{\{x \in S\}}$

Came across this notation today which I've never seen before. It was used with no explanation. For the equation to make sense, I think $\textbf{1}_{\{x \in S\}}$ means, "It takes the value 1 for $x \in S$ and $0$ otherwise." I.e., it is like an…
kanso37
  • 358
2
votes
1 answer

Array Indexing Notation Trouble

Currently I am reading "The Hundred-Page Machine Learning Book" and ran into some notation issues. The book states the following: A variable can have two or more indices, like this: $x^{(j)}_i$ or like this $x^{(k)}_{i,j}$. For example, in neural…
Mason
  • 23
  • 4
2
votes
2 answers

Prove that $\sqrt{n(n + 1)} \leq n + \frac{1}{2}$ for all $n \in \mathbb{N}$

Is it valid to say that since $\sqrt{n(n + 1)} > 1$ and $n + \frac{1}{2} > 1$ that we can square both sides without having to assume anything about their inequality? Also can someone show me how with induction or strong induction?
mk3009hppw
  • 155
2
votes
0 answers

Formal notation for repeating symbols

I am doing some work in NLP and I am not sure what the mathematical notation is for "repeating symbols inside sequences". Let me give an example using Python. In python we can simply do this: >>>'c'*5 + 'a'*3 'ccccccaaa' Now my question is very…
Astrid
  • 722
2
votes
2 answers

Notation for set of concatenated vectors?

A standard way of writing concatenation of two vectors $x\in \mathbb{R}^{m}$ and $y\in \mathbb{R}^n$ is $[x^\top, y^\top]^\top\in \mathbb{R}^{m+n}$. Let $x\in X\subset \mathbb{R}^n$ and $y\in Y \subset \mathbb{R}^m$. Then, $[x^\top, y^\top]^\top\in…
Angelos
  • 353
2
votes
0 answers

What is the difference between $=$ and $:=$?

I've encountered several usages of $:=$, for example here $$\alpha_i := \begin{cases} x_i & i \leq n \\ A & n< i \leq 2^k \end{cases}$$ and here Since $f$ is not constant, there exist some $a,b \in A$, $a \neq b$ such that $f(a) \neq f(b)$.…
Stokolos Ilya
  • 3,371
2
votes
2 answers

Notation question: $\mid $

I have the following problem: In this problem all variables range over $Z$, the set of all integers. a. Prove that if $a \mid b$ and $a \mid c$, then $a\mid (b + c)$. b. Prove that if $ac \mid bc$, and $c \neq 0$, then $a \mid b$. This question…
computersciencesayswhat
  • 31
2
votes
2 answers

Vector indexes.

For a vector of two dimensions I can use $\vec x = (x_a, x_b)$ or $\vec x = (x_x, x_y)$, if no letters are more appropriate. What if I need to name more dimensions than letters in the alphabet? What's better, $\vec x = (x_0, x_1, x_2, ... x_{29})$,…
85579
  • 5
2
votes
0 answers

Meaning of notation "$\overline{ran}$", as in "$\overline{ran \rho}\subset\overline{ran\sigma}$" (from an article about quantum entropy)

When I look up to an article about quantum entropy, I found this "$\overline{ran}$" notation. When I try to search on google about "Ran" in mathematics, it leads me to the Ran space, but I'm sure that's not what I'm looking for. So, what does the…
I Gde Daffananda
  • 21
2
votes
1 answer

Subscripts and superscripts -- universal convention?

Maybe this is because of my lack of mathematical maturity, but one of the most annoying aspects of mathematics in college or in applied fields (like finance and economics) is that subscripts and superscripts are under the whim of the author and thus…
economics
  • 153
1 2 3
…
99 100