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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.

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What does the subscript $2$ mean in the expression $\min_{w} || X w - y||_2^2$?

What does the bottom $2$ mean in the following expression? $$\min_{w} || X w - y||_2^2$$
Timothy Pulliam
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Congruence, Equal, and Equivalence

I know this is very basic problem about math. But sometimes confusing. What is the difference among Equal Sign $\left(\,=\,\right)$ Congruence Sign (we saw this on number theory) $\left(\,\equiv\,\right)$ Equivalence Sign $\left(\,\iff\,\right)$
user516076
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Mathematical notation nth smallest element of a set

I want to put the following in formula-form: "$ T_i$ should be the sum of the $ b $ smallest durations out of all durations of the predecessors of $i$ (which is the set $P_i$)" Does a mathematical formulation exist to describe the "$n$-th smallest…
Lisa
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Need help with a symbol, seems like inverted $\in$.

Need help with a symbol that appears in logic notations, as it appears (for the first time, in the book) on page 2 of the book : Elements of Real Analysis, by Denlinger. The logical statement containing the symbol is stated below with its…
jiten
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a question on notation for function spaces

If $X$ is some topological space, such as the unit interval $[0,1]$, we can consider the space of all continuous functions from $X$ to $R$. This is a vector subspace of $R^X$ since the sum of any two continuous functions is continuous…
Rajesh D
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Correct typographic notation for variables with subscripts and parts of matrices?

I’m writing a scientific text and I’m trying to conform to the ISO 80000-2 standard regarding mathematical notation. After going through the standard there are still two situations I’m unsure about: Situation 1): What is the proper typesetting…
Petahanks
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For a summation where the upper limit is not pre-defined, is $T=\infty$ meaningful?

I have a function like $$G_t = \sum_{t=0}^T \gamma^t R_t$$ I'm trying to save space in the document that I'm writing. I want to comment that there are two cases, $T \in \Bbb N$ or $T = \infty$. But I know that it's improper to say that something…
Stan Shunpike
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How to read expression $\epsilon = c > 0$

I'm going through the limits in the book and here is one of the exercises: Find an open interval about $c$ on which the inequality $|f(x) - L| < \epsilon$ holds: $f(x) = mx, m > 0, L=2m, c=3, $ $\epsilon = c > 0$ Usually in these exercises…
Stanislav Bashkyrtsev
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Pi product + set builder notation - how to read

From the low-discrepancy wiki I have: $$\displaystyle \prod_{i=1}^s[a_i, b_i) = \{ \in \mathbb{R}^s : a_i \le x_i \le b_i\}$$ where $$0 \le a_i < b_i \le 1$$ How can I read it? Should I first make do a cartesian product of $[a_i,b_i)$? For example…
Darek Nędza
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how to interpret $y \mapsto F(y|x) $ is strictly increasing for each $x$

I think it means if you hold $x$ constant i.e. $x = 3$ then if you increase $y$, then $F(y|x)$ will increase. Regardless of the value of $x$ when $x$ is held constant if you increase $y$ then $F(y|x)$ will increase in value. Is this the correct…
user9903833
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Representing finite discrete space

As far as I can tell, not being a mathematician, a finite state space, ranging from 1 to 3, can be represented by a simple A={1,2,3}, its notation being correct. A question then follows: - How to represent a discrete state space, with starts at…
JDoe
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Symbol for any number within a set for proofs

I think it's simpler if I write down where I wanted to use this symbol, rather than trying to explain it in an abstract way. I'll give a simple example and then explain the actual problem I was working on. Simple example: Let $a \in \mathbb{N}$ and…
user388680
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What do stacked numbers next to a variable without parentheses represent?

What do the $r_1$ and $r_2$ mean in the below expression? $$Z_2 / Z_1 = \pi r_1^2 / t(r_2 - r_1)$$
chavenor
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Is there a notation for defining if a function is recursively defined?

Background: I'm working on a paper on high level synthesis, a method which combines the use of programming with digital circuit design. One of the methods I want to explain is called loop unrolling which makes use of concurrency to speed up…
Ólafur Dagur Skúlason
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Can someone explain this notation: $\sum_{i=1}^n r_i b_i: r_i \in \mathbb{Z}(1 \leqq i \leqq n)$

Can anyone explain what this means: $\sum_{i=1}^n r_i b_i: r_i \in \mathbb{Z}(1 \leqq i \leqq n)$ I'm just having trouble understanding the second part. My understanding so far is that $r_i$ is an element of the set of integers $\mathbb{Z}$ but I…
Jack A
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