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.
13,180 questions
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What is $\dot{\wedge}$
What is this symbol in differential geometry ?
$$\dot{\wedge}$$
Here in 2.7.46 of Differential Geometry and Mathematical Physics: Part II. Fibre Bundles, Topology and Gauge Fields by Gerd Rudolph, ...
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Terminology confusion regarding quotient topological spaces
At the moment I am learning about quotients of topological spaces and am struggling with the notion related to them. In the class we have defined the following:
Let $\left( X, \tau \right)$ be a ...
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Dot notation for multivariable functions [closed]
Imagine I have a function $f(x,y)$. If I want to define the function keeping $y$ constant and say that it belongs to a specific space over $x$, is it correct to write, for example,
$$
f(x,\cdot)\in W^{...
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Is the notation $\mathbb{R}^{< \infty}$ used anywhere? [duplicate]
I vaguely remember seeing $\mathbb{R}^{<\infty}$, or more generally $A^{<\infty}$ being used, possibly to indicate the set of finite sequences of real numbers/elements of $A$. I know that $A^{&...
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Notation for mapping angle/axis to unit quaternion
I'm an engineer writing some documentation with maths notation.
In one expression I'm writing, I need to map an axis $A \in S^2$ and an angle $\alpha \in \mathbb{R}$ to a unit quaternion representing ...
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Proposal for a symbol for hyperoperation aggregation [closed]
Mathematicians use ∑ for repeated addition and ∏ for repeated multiplication.
I’ve been exploring whether we can generalize this pattern for higher hyperoperations — such as exponentiation, tetration, ...
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$=$-sign within factorial: is this an ancient notation for the Pochhammer symbol or just a typo?
A stupid question, but in equation (4) of this paper from the 1990 (F. Beukers, J. P. Bezivin and P. Robba, An Alternative Proof of the Lindemann-Weierstrass Theorem, The American Mathematical ...
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What does $\forall x\exists x P(x)$ mean? [duplicate]
Is this even a valid formula syntactically?
Implies "for all $x$ there is an $x$" that the $\forall x$ is redundant, because obviously there is an $x$? Or is the variable in the new context (...
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On notational conventions between Bott & Tu Vs. Lee for differential forms
Since I have been introduced to differential forms, I have seen (naively speaking) when you apply the exterior derivative, you "wedge" together one additional $d$ of the variable in question ...
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Notation $\Bbb Z_{(2)}/\Bbb Z$
I have the following homework problem:
Compute $H^\bullet(Y)$, where $Y$ is the universal cover of the mapping torus space $X$ of a degree-$2$ map $S^2 \to S^2$. (Hint: $H^2(Y) \cong \Bbb Z_{(2)}/\...
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Standard names of functions defined by generalizing the power series of trigonometric and hyperbolic functions?
For integers $m$, $n$ such that $m>n\ge0$, define functions
$$
\begin{align}
h_{m,n}\left(z\right) &= \sum_{k=0}^{\infty}{\frac{z^{m\cdot k+n}}{\left(m\cdot k+n\right)!}} \\
g_{m,n}\left(z\...
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How would you explain the Kuhn-Tucker conditions in words?
I'm sorry this is a pretty basic question, but is there any chance someone could explain the Kuhn Tucker conditions for optimisation (and ideally the pre-conditions for knowing if they are necessary ...
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Complement map on $k$-subsets: standard notation?
Let $[n]=\{1,\dots,n\}$, and write $\binom{X}{k}$ for the family of all $k$-element subsets of a set $X$.
Taking complements in $[n]$ gives the bijection
$$
\binom{[n]}{k}\xrightarrow{\;S\mapsto [n]\...
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Defining an integral operator
This is a question about notation:
Suppose that $S\subset \{1,2,\cdots,n\}$. Consider the integral operator $T$ whose value at an integrable function $f:\mathbb{R}^{n}\to \mathbb{R}$ is given by
$$\...
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Why does additive inverse have a unary operator but multiplicative inverse doesn't?
Inspired by this answer to a recent question.
As you know, the additive inverse of a value $x$ can be written as $-x$. This “unary minus” operator can be interpreted as a special case of the binary ...
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