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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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Overbar over range of possible values

In a research paper I stumbled upon the formula $x =\overline{0 \dots 2^n-1}$. As far as I understand from the context of the paper this means that $x$ can have a value between $0$ and $2^n - 1$, but what does the overline mean?
Dramentiaras
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Shorthand notation for powers of logarithmic functions

I've got an assignment here, and one question is throwing me off, as I've never seen it written like this before.. $$\int\frac{\ln^3 x}{x}\ dx$$ Is this the same as $$\int\frac{(\ln x)^3}{x}\ dx\;\;?$$
Mirrana
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When should we write $\approx$ (approximately symbol)?

Suppose we have to work with approximate numbers up to the second order, i.e., with two decimal places. Now consider $a=5/3=1.\bar6\approx1.67$. Now we have to solve $$b=1+a\tag1$$ so we have to insert $a\approx1.67$ in that equation. However, I…
manooooh
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Unfamiliar notation for min

I'm reading a paper and came across some notation for a minimum that I have not seen. Given $k \in \{ 1 .. n \}$ and a function that defines $j_k$ earlier in the text, I see this notation: $$ \min_k (j_k) $$ What would the subscript on min…
FatherShawn
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Formal notation to acces tuple components

What type of widely accepted mathematical notations are available to access tuple components? For exmaple, let suppose that I want to define a predicate $P(t,a)$ to be satisfied when the 3rd element of the 8-dimensional tuple $t$ is equal to…
Robbo
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⊕: What is the meaning of the $\oplus$-symbol?

What does this mean? $$a \oplus b$$ I've seen this notation in a text about one-time-pads. Is it XOR?
user1511417
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Repeat $\le,\subset$ when starting a new line?

My question is very simple. When one sequence of inequalities or inclusions is broken into two or more lines, one should repeat the symbol $\le $ or $\subset$ when starting a new line? In particular, suppose we want to write $A_1\subset A_2\subset…
User29983
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What does $f(x)\in \Theta(g(x))$ mean?

I have recently begun to see examples of people and literature saying statements such as $f(x) \in \Theta(...)$ but what does it mean for one function to be inside or a member of another? (i.e. I understand that's probably not what it means in this…
Isky Mathews
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Map notation for sets that are a subset of the domain

Given some map $f : A \to B$, the distinction between the use of $\to$ and $\mapsto$ is usually clear: the former is to indicate the map is from $A$, the domain, to $B$, the range (or codomain), while the latter is to express the image of an…
Bilbottom
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Is $f = x^2$ or only $f(x) = x^2$ correct?

I currently study special relativity and some authors write stuff like: $$ r^\mu = \left(ct, \vec x\right) $$ This is awful since $\mathsf r$ is a vector, and $r^\mu$ ist just a single component of that vector. Now I am wondering whether something I…
Martin Ueding
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Strange Notation: $f(x,y) = \ln (x + \text {s} \space \overline {x^2 + y^2} $)

I am currently working on my first calculus assignment of the quarter, and immediately ran into a strange notation which neither my teacher discussed nor is it mentioned in any previous parts of the chapter. $f(x,y) = \ln (x + \text {s} \space…
Ryan
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Have you seen this symbol?

I am studying Digital Design and Computer Architecture by David Money Harris and Sarah L. Harris. My professor asked searching the name of this symbol. He says this symbol means to select the smallest number which is bigger than $\log N$. Please…
Aiden
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Does omitting the multiplication operator have an effect on order of operations

When you write a mathematical expression like this: $4:2(1+1)$, does the fact that the multiplication operator is not explicitly written has any bearing on the precedence? What is the order of operations in this case? Is it: $4:4=1$ (order:…
Kornelije Petak
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Mathematical notation for distinct numbers

How can I represent a set of distinct numbers in shorthand mathematical notation? In particular I am trying to write that there are 4 distinct integers $a,b,c,d$. For three numbers, I could say: $a,b,c \in \mathbb{Z} :a \not= b\not= c \not=a$;…
Crisaon
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Notation Two Headed Arrow

Does the arrow "$\twoheadrightarrow$" mean surjective? In other words, for instance, can I gain any additional information from the following statement other than $f$ being surjective: If $M$ is an $R$-module for some arbitrary ring $R$, $P$ is a…
afedder
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