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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How to denote domain and range of a function that substitutes a given interval?
I neeed to denote the range and domain of a function that subsitutes a given interval with a diffirent interval.
For example: $f ([x,y]) = [x, x + \frac{y-x}{2}]$
My thoughts were $f: [0,1] \...
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Does tetration go up or down? (and other related questions) [duplicate]
Tetration is defined as “repeated exponentiation” - that is, $2$ tetrated to $5$ is equal to $2^{2^{2^{2^2}}}$, just as $2$ exponentiated to $5$ is equal to $2\cdot{2}\cdot{2}\cdot{2}\cdot{2}$ (...
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On the definition of parameter dependent integral function
I have the following theorem about parameter dependent integral function.
Thm. Let $(X,\mathcal{M})$ a measurable space, $\mu:\mathcal{M} \to [0,+\infty]$ a positive measure, $(Y,\tau)$ a first ...
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What does this the curly brace mean in an integral [closed]
I have seen the following integral given in an answer to one of my questions:
$$
\int_{z_0}^1 \int_0^1 1\left\{y \le \dfrac{z_0}{x}\right\}dydx
$$
What do the curl braces mean in this context?
...
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Question on notation in Extremal Combinatorics
In the following image, can someone please explain in detail the meaning of the $\sum$*(n,k) for me? I don't really see why the author mentions the following:
1.) What is the significance of whether $...
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Does the Wedge Operator (^) have some meaning in Linear Programming?
I'm reading about the Cassowary algorithm - it's an iterative algorithm which draws heavily on the simplex algorithm and Linear Programming.
While reading the paper, I keep encountering the wedge ...
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Why is $\frac{p}{-q}$ written as $\frac{-p}{q}$ and not as $\frac{p}{-q}$?
I have seen in a pure mathematics book by G.H Hardy that $\frac{-p}{q}$ is equal to $\frac{p}{-q}$, but why it is taken as that why not substitute the whole equation as $\frac{p}{-q}$, also if a ...
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Notation: why $f_\lambda$ in the hook-length formula? [closed]
I just learned the hook-length formula: the number of Standard Young Tableaux of size $n$ and shape $\lambda$ is
$$\frac{n!}{\prod_\limits{x} \operatorname{hook}(x)}$$
where the product runs over all ...
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Is an infinite composition of bijections always a bijection?
Main Question
Suppose I have a sequence of real valued functions $f_1:X_0\rightarrow X_1,...,f_n:X_{n-1} \rightarrow X_n,...,$ and I then, with $\circ$ denoting function composition, define
$$g_n : ...
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Ravi Vakil's jigsaw notation of quotient groups - can it be used to "geometrically" prove theorems?
I just discovered this: Puzzling through exact sequences, a picture book when I'm learning abstract algebra.
This thing astonishes me - it demonstrates a lot of isomorphism theorems with only jigsaw ...
- 473
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Meaning of asterisk (*) in the context of hypothesis spaces
Unfortunately, the asterisk notation in a superscript (*) is used differently in many contexts, e.g., conjugate transpose, Kleene star, optimal argument. This makes the asterisk difficult to ...
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Could it make sense to think of 0, -1, and i as overloaded unary operators rather than numbers?
This thought occurred to me and I was wondering if anyone had explored it.
For example, -x = (-1)*x. We could (choosing arbitrary symbols) rewrite this as ...
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Is there a standard notation for complementary and supplementary angles?
I recently was trying to solve a complex geometric problem using trigonometry and it made me wonder - is there a standard out there for annotating supplementary and complementary angles? I want to be ...
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Name for a "functor" that does not preserve identities.
The definition of a functor $F$ between two categories $\mathcal{C}$ and $\mathcal{D}$ says that:
If $f$ is a morphism between objects $A,B \in \mathcal{C}$ then $F(f)$ is a morphism between $F(A),F(...
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Question about the seemingly different meaning of the notation $(x)$ in $k[x]$ and $k[x,y]$ [duplicate]
Background
Example: If $k$ is a field, the ideal $(x)$ is maximal in $k[x]$. In $k[x,y]$, the ideal $(x)$ is not maximal, the ideal $(x,y)$ is maximal. We have $(x)\subseteq (x,y)\subseteq k[x,y]$.
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