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.
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Dot notation for multivariable functions
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,ドル 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},ドル 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),ドル where $Y$ is the universal cover of the mapping torus space $X$ of a degree-2ドル$ 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,ドル $n$ such that $m>n\ge0,ドル 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\},ドル 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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How to write a sum over a multidimensional grid including axis shift
I'm working with a multivariate function on a D dimensional grid.
I need to write a sum over all points on the grid and also a sum in which for each dimension a shift of 1 is applied to that axis.
I'm ...
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How can I express a planar sub-graph constraint (for a 3D grid game)?
What is a mathematically precise yet terse and clear (elegant?) way of expressing the constraint on a sub-graph of nodes in a graph representing the identities of locations (elements?) in a 3x3x3 ...