# Questions tagged [notation]

Question 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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### Operations on elements of 2 sets. Similar to nested forEach loops.

Does this make sense? $$\{ p \in P_n | \{g \in \Bbb G, q \in P_n: (q * g) \in P_n \}\}$$ Intention: all $p \in P_n$ that are products of $q \in P_n$ and $g \in \Bbb G$ If not what would be the right ...
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1 vote
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### Shorthand set builder notation?

I was reading some papers and they had the following notation: $$\big\{k\big\}_{k=0}^n$$ I assume this implies that $$\big\{k\big\}_{k=0}^n = \{k \in \mathbb{WHAT} : 0 \leq k \leq n\}$$ What is $k$...
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### For $f : \mathbb{R} \to \mathbb{R}$, what is $\sup\limits_{x \in A} f(x)$ if $A=\emptyset$? [duplicate]

Let $f : \mathbb{R} \to \mathbb{R}$ and $A$ be an empty set. What is $\sup\limits_{x \in A} f(x)$ equal to? I reckon it should just be undefined or is there an alternative convention?
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### Matrix entry notation and plane coordinate notation

Let $A$ be an $m \times n$ matrix, and $a_{ij}$ a matrix entry. Usually the index $i$ indicates the row and $j$ the column of the matrix. So changing the index $i$ makes you move in the $vertical$ ...
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### Notation: function returning the element of a partition containing $x$

Suppose $Y=\{y_1,\ldots,y_m\}$ partitions the set $X=\{x_1,\ldots,x_n\}$. I would like to define a function $y: X \to Y$ which returns $y \in Y$ if and only if $x \in y$. Is there a way to write this ...
1 vote
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### What is the difference between the principal square root of $x$ and $x^{1/2}$?

Today I learned that the square root symbol ($\sqrt{}$) represents only the "principal" square root of a number. What about exponents?—if I write $x^{1/2}$, would that encompass the negative ...
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### Meaning of Big O notation with Index $[O_{\epsilon}(n^{\epsilon})]$

I found this notation in a book and can't figure what it means. I haven't found any other examples. This is $$O_{\epsilon}(n^{\epsilon})$$ One can see it in context at page $186$ of book. Anyone know ...
1 vote
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### Notation for probability density function in Bayesian context

The Bayes theorem is often quoted as, $$P(\theta|X) = \frac{P(X|\theta)P(\theta)}{P(X)}.$$ In my use case, I'm dealing with Gaussian continuous variables. So, by $P(X|\theta)$ I'm referring to the sum ...
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### Understanding random variables as functions

First of all, I have read What is a function and I have understood it basically and it is clear to me that in order to caluclate statistics "things" have to be transformed or mapped to ...
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### What is the notation of length of vector?

I am looking for a symbol to express the length of a vector or table, For example we have a vector V, len(V)==5 ( for example). How can I represent it by a symbol ?
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### Notation $(S,*)$ or $(\mathbb S,*)$ for semigroup leading to group $(\mathbb G,*)$

In a number-theoretic context, is it best to use the notation $(S,*)$ or $(\mathbb S,*)$ for a generic semigroup leading to group $(\mathbb G,*)$ by taking equivalence classes under an equivalence ...
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### The set $X$ can be seen as index set?

Let $X$ be a set, and the power set of $X$ be $\mathcal P(X).$ For $\mathcal B \subset \color{red}{\mathcal P(X)},$ does \begin{align} &\quad \ \left\{ U\subset X \mid \exists \Lambda : \mathrm{...
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### Is Euler's identity really that beautiful or is it notationally contrived to be beautiful?

When I first saw the identity $e^{i\pi} + 1 = 0$, I was awestruck at how $5$ fundamental mathematical constants could combine so elegantly, finding invariance in all their numerical chaos. It was one ...
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### notation for replacing values in one matrix with another with condition

I have two matrices of equal size. $'A'$ is a binary image, and '$B$' has values ranging between $0$ and $1$. What's the correct notation which would demonstrate that foreground elements of A (equal ...
1 vote
### Integrating w.r.t. to $\mathrm d\mu(x)$ vs $\mu(\mathrm dx)$
When integrating a function $f$ with respect to a measure $\mu$, I often see two different notations $$\int_A f(x) \mathrm d\mu(x)$$ and $$\int_A f(x) \mu(\mathrm dx)$$ How are these two different?...