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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What's the letter to denote a rational number? [closed]
I know that $x$ is used to denote a real number ($x \in \mathbb{R}$), $n$ for a natural integer ($n \in \mathbb{N}$), $k$ for a relative integer ($k \in \mathbb{Z}$), $z$ for a complex number ($z \in \...
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Can we *really* do algebraic operations involving roots on C?
With BSc in Maths and loads of grey hair, something has been on my mind for decades, and I couldn't quite enunciate it. Let me try.
Root is inherently "multi-valued" operation. So
$$
\sqrt{4}...
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Short notation for $(u_1u_2\cdots u_n)' =u_1'u_2\cdots u_n + u_1u_2'\cdots u_n+\cdots+u_1u_2\cdots u_n'$
Looking for a Short hand notation for $(u_1u_2\cdots u_n)' =u_1'u_2\cdots u_n + u_1u_2'\cdots u_n+\cdots+u_1u_2\cdots u_n'$
Or some type of a rolling signifier notation that might already exists in ...
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Can the differential be unitless while the variable have an unit in integration?
Apologies for terminology inconsistencies, as I'm reading a Chinese statistics and probabilities textbook while looking up intrinsics on an English encyclopedia.
This arose when I was reading the ...
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Must both conditions of operator "OR ($\vee$)" be defined in mathematics? [closed]
I am in the process of writing an article and to explain my question, am providing to you a smaller instance of my wondering so that you can understand it, suppose that $A=\{0,1\}$ and that I define ...
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Is there a rule for using parentheses or brackets after the summation symbol to indicate what is included in the sum? [duplicate]
Using parentheses or brackets removes ambiguity but is it necessary?
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Exponentiation of a linear operator
I am trying to go through "Introduction to Functional Analysis" from MITOCW (MATH 18.102) by myself and I am confused by a question in the second problem set.
Let $B$ be a Banach space. Let $...
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Summation of arithmetic series [closed]
How to represent a sum of $n$ items of an arithmetic series with the use of the sigma notation?
For the sum of the 10 first items, is the below one correct?
$$
\color{gray}{
\sum_{\{{x_i: x_{i-1}+k \}}...
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Are there terminologies for "one-to-one" but not "onto" functions, and "onto" but not "one-to-one" functions?
One-to-one (injective) functions are not necessarily not onto (not surjective).
Similarly, onto functions are not necessarily not one-to-one.
So, a function can be one-to-one and onto (bijective).
$f(...
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meaning of $IBr(X | Q)$
In the paper 1, there is a notation used without specifying the meaning.
It is $IBr(X | Q)$ in Definition $4.1$. What it means? Irreducible Brauer characters of the group X from a block with defect ...
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Question about notation in Durrett's book
I have been studying Markov Chains through Rick Durrett's book, more precisely I was focusing on the Markov Property (Theorem 5.2.3 on page 276 of the book available at: https://services.math.duke.edu/...
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If I have a sequence $a_0, a_1, a_2, \cdots$ , then is expressing the limit of this sequence as $a_\omega$ sensible?
If I have a sequence created by some rule which comes to a limit , then I can express it as $a_0, a_1,a_2,\cdots$.
If I said $\lim_{n \to \infty} a_n = a_{\omega} $ , is that a sensible thing to do ?
...
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Further questions about correspondence theorem for rings and quotient ring isomorphism.
Background
This is a continuation of a post about correspondence theorem for rings, I will repost what I have written here from the Background section of that post here for ease of reference:
The ...
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Notation question related to an exercise from Dummit & Foote in polynomial rings section
Background
Exercise: Let $F[x,y_1,y_2,\ldots]$ be the polynomial ring in the infinite set of variables $x,y_1,y_2,\ldots$ over the field $F$, and let $I$ be the ideal $(x-{y_1}^2, y_1-{y_2}^2,\ldots,...
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Notation of Expected value, when game with loss function and strategy as variable.
I have the case where I need to write the expected value of a score $\mathbb{E}[S]$ in a game where we can use different strategies $\sigma$ and also the loss function $f$ may change, which I write ...
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