Mathematics Stack Exchange
Mathematics Stack Exchange

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.

Before asking a question on the site, please check if you can find your answer in Earliest Uses of Various Mathematical Symbols or the book A History of Mathematical Notations.

Alternatively, a textbook or paper usually takes the time to explain the notation they're using; please remember to mention where you've seen the notation you are asking about.

12848 questions
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How to read "Upper closure operator" definition

I a book the "Upper closure operator" definition is given by: I do understand the concept of the Upper closure operator. But I cannot figure out how to read the last line. Could someone explain it? Thank you.
sky_e
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Term for "relative-orthogonality" of two random binary vectors

We expect two random bipolar vectors $x,y\in\{-1,1\}^n$ to have dot product of $0$ such that: $\mathbb{E}[x \cdot y]=0$. Accordingly, these vectors are termed "orthogonal". Is there any term for the relationship of two random binary vectors…
user160623
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Understanding a question in algebra

Does the equality $\lfloor nx \rfloor = n\lfloor x \rfloor$ hold for the integers $n\ge 2$? What does this sign "$\lfloor$" and " $\rfloor$" sign mean in this context? Thanks!
Luthier415Hz
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"Extended" set notation

Let two sets $\mathcal{A} \subset \mathbb{R}^2 = \left \{ (x_1,x_2) | x_1,x_2 \in \mathbb{R} \right \} $ and $\mathcal{B} \subset \mathbb{R}^3 = \left \{ (x_1,x_2,x_3) | x_1,x_2,x_3 \in \mathbb{R} \right \}$ How can I mathematically write that…
Cristi
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symbols for exponentiation

In thinking about this question on PLDI I wondered if there are any other mathematical symbols which represent exponentiation as an infix operator. x pow y --> xy Commonly used notations in programming are caret ^ (which often has other meanings…
Bruce Adams
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What exactly does this notation in an old letter mean?

This is from a letter sent around 1859: I think the curly braces are just to be treated like parentheses, so that part is fine (if that's not the case, do tell), but I struggle to understand what that dot represents. From context I would assume…
Outis Nemo
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Mathematical notation for the least value a function can give

I have a set with unknown cardinality. The cardinality can be from a number a to a number b. How can I indicate the number a (or b)? The question in texts is: "What is the least value of n(A)" (A is a set with a few possible cardinalities) How can I…
Pooia
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Guidance on notation for logic and sets

I have been learning more about sets lately and have stumbled upon notation (or I guess a language) such as this: I would like to know the name of this notation and perhaps some resources to learn it.
Official Pyramid
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Symbol for "not always equal"?

Updated post with better context: I can do what I need to do using words. I am just trying to understand if there's notation I could use instead that would communicate this concept conclusively. The metric should be: There should be no doubt…
martin's
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The two kinds of a Cartesian product and how to specify which is used?

I have already asked a similar question, but it appears I must ask a more fundamental question about Cartesian products. In my experience, we normally notate in accordance with this expression: $$(s_1,s_2,\ \dots , s_n) \in S^n \tag1$$ However, some…
user110391
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How to denote a set of tuples of tuples of...?

This question already exists, but its answer was not helpful to me. If the elements of a set are of the form $((a,b),(c,d))$ (the elements are pairs of pairs), and the like, how does one denote that? A set of $n$-tuples consisting of numbers all…
user110391
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How to define a set of $n$ such that $\mathbf{X}_{n,m}=1$ for at least one $m$?

Given a matrix $\mathbf{X}\in\{0,1\}^{N\times M}$, what is the set notation I should use to define this: the set of all $n\in\{1,\ldots,N\}$ such that there exists at least $m\in\{1,\ldots,M\}$ where $\mathbf{X}_{n,m}=1$. I write it as:…
zdm
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Notate the value of a function f'(x) for a certain interval of x

I'm currently working on a homework assignment where we have to describe certain characteristics of the graph of a function f. I'm trying to describe that the value of the derivative function f' is f'(x) < 0 for x < 2 and f'(x) > 0 for x > 2. I'm…
Laszlo Stark
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Symbol to distinguish same variable for two different groups

Consider I have two groups: control and treatment. The mean for glucose variable is written as $\mu_g$ How can I write mean for glucose for the control group and treatment group in mathematical notation? I want to avoid using superscript e.g.…
Kay
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Symbology check (specially bijective sets)

Imagine I have a set $\mathbb{P}$ with subsets $\mathbb{P_1}, \mathbb{P_2}$, and a multiset $D$. I need to write that one of the subsets bijects the multiset and the other one does not belong to the multiset not taken from the first one. So, an…
Ian Barquette
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