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.

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What is the name for this operator, and how can it be applied to multiple variables within the same equation?

My question is in two parts; the first is, what is the $|$ operator called? Here's an example of it in use: $$(x + 5)|_{x=3} = 8$$ My second question is, how do I use this operator for more than one variable? For example, would I write $(x +…
Cisplatin
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Need help solving A×((B×C)×D) in index notation

How do I solve A×((B×C)×D) in index notation? I ended up with three Levi-Civita symbols and have no idea how to contract them. Thanks for the help!
Anne
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Clarification on use of sigma notation

I find the use of sigma notation quite arbitrary. Sometimes the counters and limits are defined, sometimes they aren't. And sometimes, I just can't comprehend what it means. For example, in my textbook, they've given an example, $$\alpha^3 +…
Gerard
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What does $R^+$ mean?

I'm not sure if it's statistics related but I came over this in my stats related computing assignment. Does $R^+$ (looks like R to the power of plus) mean all positive real numbers? Does it include 0?
hax13
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Why are certain greek characters used predominantly for certain purposes in mathematics?

For example, $\epsilon$ and $\delta$ are used in Real Analysis for proving limits... $\phi$, $\nu$ and $\mu$ were introduced to me in the context of number theory... and then $\pi$ is used for purposes other than its canonical $3.14...$ value, such…
Mirrana
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What is $\mathbf{a}^\bot=(\alpha, \beta)^\bot=(\beta, -\alpha)$ notation?

I stumbled upon this notation in a book and I cannot find a reference on what this can mean: $\mathbf{a}^\bot=(\alpha, \beta)^\bot=(\beta, -\alpha)$ Here is where I found it:
Trident D'Gao
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Can we use $\land$, $\lor$ and $\lnot$ outside logic?

In most parts of mathematics I've seen logical symbols like $\implies, \exists, \forall$, etc. But I haven't seen $\land, \lor, \lnot$. Like " $\forall x\in\mathbb{R} \land y>0$ " instead of " $\forall x\in\mathbb{R}$ and $y>0$ ". Is there any…
jinawee
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What's the notation for a definition that meets certain constraints.

I'm writing a lengthy proof in which I am stating the proof in prose and then in mathematical symbols. But I don't know the notation to define a symbol that meets certain constraints. In the following example I've used min and max to get around my…
Michael Deardeuff
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Symbol to Break Steps to Solve Equation Apart in the Same Line?

Is there a symbol for solving an equation that breaks each step? Usually this is done as a new line, like the following: 4x + 2 = 5 4x = 3 x = 3/4 I'm looking for a universal symbol that could change the above to look like this: 4x + 2 = 5…
Keavon
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What is the proper notation when defining certain functions?

What is the proper notation when defining certain functions? For example, consider the function $\phi:\mathbb{Q} \rightarrow \mathbb{Z}\times\mathbb{N}$ defined by $\phi(\frac{p}{q})=(p,q)$ for any $\frac{p}{q}\in\mathbb{Q}$ such that p and q have…
Manuel Osuna
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"Z Notation Bag Membership": What does this represent in math?

In the glossary for mathematical operators in Unicode1, the last one, u+22FF "⋿", is said to represent "Z Notation Bag Membership". Looking up "z notation bag membership" gives me this info: The symbol "Z Notation Bag Membership" is included in the…
CrSb0001
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Defining a set of prime numbers up to index $m$.

I want to define a set of prime numbers up to index $m$ as follows $$P_m=\{p_i:p_1\leq p_i\leq p_m,i\in \mathbb N\}$$ Now, $m=1,2,3,...$ should define the cardinality of this set. I like this compactness but am concerned that the $i\in\mathbb N$…
Nicojwn
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Mean and Standard Deviation of a Set in Set-Builder Notation

Say we have set $C_{mc} = \{ x_1, x_2, \dots, x_n \}$ and we want to show a calculation of the mean ($\mu_c$) and the standard deviation ($\sigma_c$) for this set. Do the following equations make sense? Or is there a better way to show this using…
Jordan Gleeson
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Notations for 'difference of change' or 'change of change

In my thermodynamics class, I came across an equation: $$\Delta S_2 - \Delta S_1 = C_v\ln\frac{T_2}{T_1}$$ And many equations involving changes of two changes. Now my question is do mathematicians have any neat notations to represent such…
Akilan SS
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Math notation for sum of the last $n$ numbers in a vector

I have a vector of numbers, $x_0, x_1, x_2, \dots, x_n$. I'm trying to figure out how I can denote the sum of the last 3 numbers in the vector. For example, consider the vector: x = [1, 2, 3, 4, 5, 6] I'm looking for the notation that produces,…
turtle
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